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All Textbook Solutions for Precalculus
For Exercises 83-94, factor the trinomials. (See Examples 6-8) 2t328t2+80t86PEFor Exercises 83-94, factor the trinomials. (See Examples 6-8) 7y3z40y2z212yz3For Exercises 83-94, factor the trinomials. (See Examples 6-8) 11a3b+18a2b28ab3For Exercises 83-94, factor the trinomials. (See Examples 6-8) t218t+81For Exercises 83-94, factor the trinomials. (See Examples 6-8) p2+8p+16For Exercises 83-94, factor the trinomials. (See Examples 6-8) 50x3+160x2y+128xy2For Exercises 83-94, factor the trinomials. (See Examples 6-8) 48y372y2z+27yz2For Exercises 83-94, factor the trinomials. (See Examples 6-8) 4c420c2d3+25d6For Exercises 83-94, factor the trinomials. (See Examples 6-8) 9m4+42m2n4+49n8For exercises 95-106, factor the binomials. (see Examples 9-10) 9w264For exercises 95-106, factor the binomials. (see Examples 9-10) 16t24997PEFor exercises 95-106, factor the binomials. (see Examples 9-10) 75m627n4For exercises 95-106, factor the binomials. (see Examples 9-10) 625p416For exercises 95-106, factor the binomials. (see Examples 9-10) 81z41101PE102PEFor exercises 95-106, factor the binomials. (see Examples 9-10) c427cFor exercises 95-106, factor the binomials. (see Examples 9-10) d48d105PEFor exercises 95-106, factor the binomials. (see Examples 9-10) 27m1264n9For exercises 107-130, factor completely. (see Examples 11-13) 30x4+70x3120x2280x108PEFor exercises 107-130, factor completely. (see Examples 11-13) a2y2+10y25110PEFor exercises 107-130, factor completely. (see Examples 11-13) x2223x2228For exercises 107-130, factor completely. (see Examples 11-13) y2+22+5y2+224113PEFor exercises 107-130, factor completely. (see Examples 11-13) y3+34249For exercises 107-130, factor completely. (see Examples 11-13) x+y3+z3For exercises 107-130, factor completely. (see Examples 11-13) a+53b3117PE118PE119PEFor exercises 107-130, factor completely. (see Examples 11-13) d+624d32121PEFor exercises 107-130, factor completely. (see Examples 11-13) t1+27t4t327For exercises 107-130, factor completely. (see Examples 11-13) m6+26m327124PEFor exercises 107-130, factor completely. (see Examples 11-13) 16x6z+38x3z54z126PEFor exercises 107-130, factor completely. (see Examples 11-13) x2y2x+y128PE129PE130PEFor Exercises 131-142, Factors completely. Write the answer with positive exponents only. (See Example 14) 2x47x3+x2132PE133PE134PEFor Exercises 131-142, Factors completely. Write the answer with positive exponents only. (See Example 14) 2c7/4+4c3/4136PE137PE138PEFor Exercises 131-142, Factors completely. Write the answer with positive exponents only. (See Example 14) 5x3x+12/3+3x+15/3For Exercises 131-142, Factors completely. Write the answer with positive exponents only. (See Example 14) 7t4t+13/4+4t+17/4141PE142PEExplain the similarity in simplifying the given expressions. a.3x+24x7b.3x+24x7Explain the similarity in simplifying the given expressions. a.x+3x3b.x+3x3Why is the sum of squares a2+b2 not factorable over the real number?Explain the similarity in the process to factor out the GCF in the following two expressions. 5x4+4x3and5x4+4x3147PE148PE149PEWe say that the expression x24 is factorable over the integers as x+2x2 . Notice that the constant terms in the binomials are integers. The expression x23 can be factored over the irrational as x23=x+3x3 . For Exercises 147-152, factor each expression over the irrational numbers. w449151PEWe say that the expression x24 is factorable over the integers as x+2x2 . Notice that the constant terms in the binomials are integers. The expression x23 can be factored over the irrational as x23=x+3x3 . For Exercises 147-152, factor each expression over the irrational numbers. c223c+3For Exercises 153-156, determine if the statement is true or false. If a statement is false, Explain why. The sum of two polynomials each of degree 5 will be degree 5.For Exercises 153-156, determine if the statement is true or false. If a statement is false, Explain why. The sum of two polynomials each of degree 5 will be less than or equal to degree 5.For Exercises 153-156, determine if the statement is true or false. If a statement is false, Explain why. The product of two polynomials each of degree 4 will be degree 8.For Exercises 153-156, determine if the statement is true or false. If a statement is false, Explain why. The product of two polynomials each of degree 4 will be less than degree 8.Many expressions in algebra look similar but the methods used to simplify the expressions may be different. For exercises 1-14, simplify each expression. Assume that the variables are restricted so that each expression is defined. a.641/2b.641/3c.642/3d.641e.641/2f.641/2g.642/3h.642/32PRE3PRE4PRE5PREMany expressions in algebra look similar but the methods used to simplify the expressions may be different. For exercises 1-14, simplify each expression. Assume that the variables are restricted so that each expression is defined. a.3a+4b22ab2b.3a+4b22ab27PRE8PREMany expressions in algebra look similar but the methods used to simplify the expressions may be different. For exercises 1-14, simplify each expression. Assume that the variables are restricted so that each expression is defined. a.x+2forx2b.x+2forx210PREMany expressions in algebra look similar but the methods used to simplify the expressions may be different. For exercises 1-14, simplify each expression. Assume that the variables are restricted so that each expression is defined. a.2x32x3b.2x3+2x312PRE13PREMany expressions in algebra look similar but the methods used to simplify the expressions may be different. For exercises 1-14, simplify each expression. Assume that the variables are restricted so that each expression is defined. a.62+82b.62+82Determine the restrictions on the variable. a.x+4x3b.5c216c.67ab3Simplify. a.x28xx27x8b.3+9563SP4SPSubtract the rational expressions and simplify the result. tt2+5t+62t2+3t+2Simplify. 17+1yy77y7SPSimplify. 51+hh59SPA expression is a ratio of two polynomials.2PE3PEThe ratio of a polynomial and its opposite equals .5PE6PEFor Exercises 7 – 14, determine the restrictions on the variable. (See Example 1) x4x+7For Exercises 7-14, determine restrictions on the variable. (See Example 1) y1y+10For Exercises 7-14, determine the restrictions on the variable. (See Example 1) aa281For Exercises 7-14, determine the restrictions on the variable. (See Example 1) tt216For Exercises 7 – 14, determine the restrictions on the variable. (See Example 1) aa2+8112PE13PE14PEDetermine which expressions are equal to 5x3 . a.5x3 b.53x c.53x d.53x16PE17PEFor Exercises 17-26, simplify the expression and state the restrictions on the variable. (See Example 2) y264y27y8For Exercises 17-26, simplify the expression and state the restrictions on the variable. (See Example 2) 12a2bc3ab5For Exercises 17-26, simplify the expression and state the restrictions on the variable. (See Example 2) 15tu5v3t3u21PE22PEFor Exercise 17-26, simplify the expression and state the restrictions on the variable. (See Example 2) 2y216y64y2For Exercises 17-26, simplify the expression and state the restrictions on the variable. (See Example 2) 81t27t263t25PE26PEFor Exercises 27-34, multiply or divide as indicated. The restrictions on the variable are implied. (See Example 3) 3a5b7a5b2a10b12a4b10For Exercises 27-34, multiply or divide as indicated. The restrictions on the variables are implied. (See Example 3) 8x3yx3y46xy824x9y29PEFor Exercise 27-34, multiply or divide as indicated. The restrictions on the variables are implied. (See Example 3) m11n2m2n218m9n59m2+6mn15n2For Exercise 27-34, multiply or divide as indicated. The restrictions on the variables are implied. (See Example 3) 2a2bab28b2+aba2+16ab+64b22a2+15ab8b232PEFor Exercises 27-34, multiply or divide as indicated. The restrictions on the variables are implied. (See Example 3) x36416xx32x2+8x+32x2+2x8For Exercises 27-34, multiply or divide as indicated. The restrictions on the variables are implied. (See Example 3) 3y2+21y+14725yy3y3343y212y+3535PE36PEFor Exercises 35-40, identify the least common denominator for each pair of expressions. 2t+1(3t+4)3(t2)and4t(3t+4)2(t2)38PE39PE40PEFor Exercises 41-56, add or subtract as indicated. (See Example 4-5) m2m+3+6m+9m+342PEFor Exercises 41-56, add or subtract as indicated. (See Examples 4-5) 29c+715c344PEFor Exercises 41-56, add or subtract as indicated. (See Examples 4-5) 92x2y411xy546PE47PEFor Exercises 41-56, add or subtract as indicated. (See Examples 4-5) 4m23m49PE50PEFor Exercise 41-56, add or subtract as indicated. (See Examples 4-5) 5y+2y+16y2For Examples 41-56, add or subtract as indicated. (See Examples 4-5) 5t2+4t+23t53PEFor Exercises 41-56, add or subtract as indicated. (See Examples 4-5) 2x1x7+x+67x55PE56PEFor Exercises 57-68, simplify the complex fraction. (See Example 6-8) 127x+1913+19x58PE59PEFor Exercises 57-68, simplify the complex fraction. (See Examples 6-8) x32x+33x13+13x61PE62PE63PEFor Exercises 57-68, simplify the complex fraction. (See Examples 6-8) 41+h4hFor Exercises 57-68, simplify the complex fraction. ( See Examples 6-8_ 7x+h7xh66PE67PEFor Exercises 57-68, simplify the complex fraction. (See Examples 6-8) 1x+15x23x4+1x4For Exercises 69-84, simplify the expression. Assume that the variable expressions represent positive real numbers. (See Example 9) 4yFor Exercises 69-84, simplify the expression. Assume that the variable expressions represent positive real numbers. (See Example 9) 7zFor Exercises 69-84, simplify the expression. Assume that the variable expressions represent positive real numbers. (See Example 9) 7y3For Exercises 69-84, simplify the expression. Assume that the variable expressions represent real numbers. (See Example 9) 7z4For Exercises 69-84, simplify the expression. Assume that the variable expressions represent positive real numbers. (See Examples 9) 12x+1For Exercises 69-84, simplify the expression. Assume that the variable expressions represent positive real numbers. (See Example 9) 50x2For Exercises 69-84, simplify the expression. Assume that the variable expressions represent positive real numbers. (See Example 9) 81511For Exercise 69-84, simplify the expression. Assume that the variable expressions represent positive real numbers. (See Example 9) 1262For Exercises 69-84, simplify the expression. Assume that the variable expressions represent positive real numbers. (See Example 9) x5x+5For Exercises 69-84, simplify the expression. Assume that the variable expressions represent real numbers. (See Example 9) y3y+3For Exercise 69-84, simplify the expression. Assume that the variable expressions represent positive real numbers. (See Example 9) 210+35410+25For Exercises 69-84, simplify the expression. Assume that the variable expressions represent positive real numbers. (See Example) 33+65326For Exercises 69-84, simplify the expression. Assume that the variable expressions represent positive real numbers. (See Example 9) 73x+3xx82PEFor Exercises 69-84, simplify the expression. Assume that the variable expressions represent positive real number. (See Example 9) 5w77wFor Exercises 69-84, simplify the expression. Assume that the variable expressions represent positive real numbers. (See Example 9) 13t22tThe average round trip speed 5 (in mph) of a vehicle travelling a distance of a miles each way is given by s=2ddr1+dr2 . In this formula, r1 is the average speed going one way, and r2 is the average speed on the return trip. a. Simplify the complex fraction. b. if a phone files 400 mph from Orland to Albuquerque and 460 mph on the way back, compute the average speed of the round trip. Round to 1 decimal place.The formula R=11R1+1R2 gives the total electrical resistance R (in ohms, ) when two resistors of resistance R1 and R2 are connected in parallel. a. Simplify the complex fraction. b. Find the total resistance when R1=12 andR2=20 .87PE88PEFor Exercises 89-102, simplify the expression. 2x3yx2y+3xyx2+6x+92x+65xy490PEFor Exercises 89-102, simplify the expression. 42t+1t2t2+17t+8(t+8)92PE93PEFor Exercises 89-102, simplify the expression. c2+13c+18c29+c+1c+3c+8c395PE96PEFor Exercises 89-102, simplify the expression. 3425398PE99PEFor Exercises 89-102, simplify the expression, 105010101PEFor Exercises 89-102, simplify the expression. m412mm+2103PE104PE105PEFor Exercises 103-110, write the expression a single tern, factored completely. Do not rationalize the denominator. 2x+x107PE108PEFor Exercises 103-110, write the expression as a single term, factored completely. Do not rationalize the denominator. 24x2+9+8x24x2+9110PE111PE112PEThe numbers 1,2,3,4,5,10,and 20 are natural numbers that are factors of 20. There are other factors of 20 within the set of national numbers and the set of irrational numbers for example: a. Show that 143and307 are factors of 20 over the set of rational numbers. b. show that 55 and 5+5 are factors of 20 over the set of irrational numbers.114PEFor Exercises 115-120, simplify the expression. w3n+1w3nzwn+2wnz2116PEFor Exercises 115-120, simplify the expression. 523118PE119PEFor Exercises 121-122 rationalize the numerator by multiplying numerator and denominator by the conjugate of the numerator. x+yx3+y3121PEFor Exercises 121-122 rationalize the numerator by multiplying numerator and denominator by the conjugate of the numerator. x+hxhSolve. 5v42=2v73Identify each equation as a conditional equation, a contradiction, or an identity. Then give the solution set. a.4x+1x=6x2b.25x=1=2x12x+6c.23x1=6x+18Solve the equation. 103x213x=40Solve the equation by using the square root property. a.a2=49b.t+42=24Solve the equation by completing the square and applying the square root property. 3x224x6=0Solve the equation by applying the quadratic formula. xx8=3Solve the equation and check the solution. 15y=213y+2Solve. 3xx5=2x+1+2x2+40x24x5Solve the equations. a.524t=50b.5=6c7+9Solve the equations. a.3x4=2x+1b.4+x=4xSolve the equation. t+7=t5Solve. 1+n+4=3n+1Solve the equation. 2x43/4=54Solve for v. E=12mv2v0Solve for p.cp2dp=kA equation is a second-degree equation of the form ax2+bx+c=0 where a0 .A equation is a first-degree equation of the form ax+b=0 where a0 .A equation is one that is true for some values of the variable and false for others.An is an equation that is true for some values of the variable for which the expression in the equation are defined.A .is an equation that is false for all values of the variable.The square root property indicates that if x2=k, then x= .Given ax2+bx+c=0(a0), write the quadratic formula.A equation is an equation in which each term contains a rational expression.For Exercises 9-20, solve the equation. (See Example 1) 4=73(4t+1)For Exercises 9-20, solve the equation. (See Example 1) 11=72(5p2)For Exercises 9-20, solve the equation. (See Example 1) 6v2+3=9(v+4)For Exercises 9-20, solve the equation. (See Example 1) 5u4+2=11u3For Exercises 9-20, solve the equation. (See Example 1) 0.05y+0.02(6000y)=270For Exercises 9-20, solve the equation. (See Example 1) 0.06x+0.04(10,000x)=520For Exercises 9-20, solve the equation. (See Example 1) 2(5x6)=4[x3(x10)]For Exercises 9-20, solve the equation. (See Example 1) 4(y3)=3[y+2(y2)]For Exercises 9-20, solve the equation. (See Example 1) 12w34=23w+2For Exercises 9-20, solve the equation. (See Example 1) 25p310=715p1For Exercises 9-20, solve the equation. (See Example 1) n+34n25=n+1101For Exercises 9-20, solve the equation. (See Example 1) t23t+75=t410+2In the mid-nineteenth century, explorers used the boiling point of water to estimate altitude. The boiling temperature of water T(inF) can be approximated by the model T=1.83a+212, where a is the altitude in thousands of feet. a. Determine the temperature at which water boils at an altitude of 4000ft. Round to the nearest degree. b. Two campers hiking in Colorado boil water of tea. If the water boils at 193F, approximate the altitude of the campers. Give the result to the nearest hundred feet.For a recent year, the cost C(in$) for tuition and fees for x credit-hours at a public college was given by C=167.95x+94 . a. Determine the cost to take 9 credit-hours. b. If Jenna spent $2445.30 for her classes, how many credit-hours did she take?For Exercises 23-28, identify the equation as a conditional equation, a contradiction, or an identity. Then give the solution set. (See Example 2) 2x3=4(x1)12xFor Exercises 23-28, identify the equation as a conditional equation, a contradiction, or an identity. Then give the solution set. (See Example 2) 435n+1=4n816nFor Exercises 23-28, identify the equation as a conditional equation, a contradiction, or an identity. Then give the solution set. (See Example 2) 62w=4w+12w10For Exercises 23-28, identify the equation as a conditional equation, a contradiction, or an identity. Then give the solution set. (See Example 2) 5+3x=3x12For Exercises 23-28, identify the equation as a conditional equation, a contradiction, or an identity. Then give the solution set. (See Example 2) 12x+3=14x+1For Exercises 23-28, identify the equation as a conditional equation, a contradiction, or an identity. Then give the solution set. (See Example 2) 23y5=16y4For Exercises 29-36, solve by applying the zero-product property. (See Example 3) n2+5n=24For Exercises 29-36, solve by applying the zero-product property. (See Example 3) y2=187yFor Exercises 29-36, solve by applying the zero-product property. (See Example 3) 8tt+3=2t5For Exercises 29-36, solve by applying the zero-product property. (See Example 3) 6mm+4=m15For Exercises 29-36, solve by applying the zero-product property. (See Example 3) 3x2=12xFor Exercises 29-36, solve by applying the zero-product property. (See Example 3) z2=25zFor Exercises 29-36, solve by applying the zero-product property. (See Example 3) m+4m5=8For Exercises 29-36, solve by applying the zero-product property. (See Example 3) n+2n4=27For Exercises 37-42, solve by using the square root property. (See Example 4) x2=81For Exercises 37-42, solve by using the square root property. (See Example 4) w2=121For Exercises 37-42, solve by using the square root property. (See Example 4) 5y235=0For Exercises 37-42, solve by using the square root property. (See Example 4) 6v230=0For Exercises 37-42, solve by using the square root property. (See Example 4) k+22=28For Exercises 37-42, solve by using the square root property. (See Example 4) 3z+11210=110For Exercises 43-48, determine the value of n that makes the polynomial a perfect square trinomial. Then factor as the square of a binomial. x2+14x+nFor Exercises 43-48, determine the value of n that makes the polynomial a perfect square trinomial. Then factor as the square of a binomial. y2+22y+nFor Exercises 43-48, determine the value of n that makes the polynomial a perfect square trinomial. Then factor as the square of a binomial. w23w+nFor Exercises 43-48, determine the value of n that makes the polynomial a perfect square trinomial. Then factor as the square of a binomial. v211v+nFor Exercises 43-48, determine the value of n that makes the polynomial a perfect square trinomial. Then factor as the square of a binomial. m2+29m+nFor Exercises 43-48, determine the value of n that makes the polynomial a perfect square trinomial. Then factor as the square of a binomial. k2+25k+nFor Exercises 49-54, solve by completing the square and applying the square root property. (See Example 5) y2+22y4=0For Exercises 49-54, solve by completing the square and applying the square root property. (See Example 5) x2+14x3=0For Exercises 49-54, solve by completing the square and applying the square root property. (See Example 5) 2xx3=4+xFor Exercises 49-54, solve by completing the square and applying the square root property. (See Example 5) 5cc2=6+3cFor Exercises 49-54, solve by completing the square and applying the square root property. (See Example 5) 4y212y+5=0For Exercises 49-54, solve by completing the square and applying the square root property. (See Example 5) 2x214x+5=0For Exercises 55-64, solve by using the quadratic formula. (See Example 6) x23x7=0For Exercises 55-64, solve by using the quadratic formula. (See Example 6) x25x9=0For Exercises 55-64, solve by using the quadratic formula. (See Example 6) 6x+5x3=2x7x+5+x12For Exercises 55-64, solve by using the quadratic formula. (See Example 6) 5c+72c3=2cc+1535For Exercises 55-64, solve by using the quadratic formula. (See Example 6) 12x227=514xFor Exercises 55-64, solve by using the quadratic formula. (See Example 6) 13x276=32xFor Exercises 55-64, solve by using the quadratic formula. (See Example 6) 0.4y2=2y2.5For Exercises 55-64, solve by using the quadratic formula. (See Example 6) 0.09n2=0.42n0.49For Exercises 55-64, solve by using the quadratic formula. (See Example 6) m2+4m=2For Exercises 55-64, solve by using the quadratic formula. (See Example 6) n2+8n=3For Exercises 65-66, determine the restrictions on x . 3x5+2x+4=57For Exercises 65-66, determine the restrictions on x . 2x+15x7=23For Exercises 67-84, solve the equation. (See Examples 7-8) 1272y=5yFor Exercises 67-84, solve the equation. (See Examples 7-8) 1343t=7t