If we are told that (x - 8)(x + 3) = 0, then what can we infer? By the zero product property we know: = 0 OR =0 And therefore we know that: OR x =

Q: 3. Factor x – 21 x – 20 completely by using synthetic division if one of the factors is (x + 4)

A: Consider the given expression as x3-21x-20 and one linear factor is x+4. Equate the linear factor to…

Q: The polynomial + ax 3x+ hx 2 has roots -1 and 2. one of which is a triple root. Find the values of a…

A: There are two possible case, checking one by one both to know which is the possible case as in next…

Q: What polynomial must be added to-7x3+8x-3 so that the sum is x2-x-1?

A:

Q: Show that (x- 3) is a factor of 2.x3 - 2x2 - 17x + 15. Hence express 2x³ – 2.x² – 17x + 15 in the…

A:

Q: 2. If the result of a polynomial division is 2x – 4x? – 5x + x+2 23 ,make at least three definitive…

A: Consider the given: If the result of the polynomial division is-2x3−4x2−5x+23x+2It means , The…

Q: If  x3 + 7x - a has a remainder of 1 when divided by x+1 then a has a value of __?

A: Please refer the attached image for complete solution.

Q: (10x-22) (3x+7) X15 "Theorem:

A: Given:

Q: The polynomial 2x^3 + ax^2 - 10x + b has a factor of ( x-1 ) and has a remainder of 15 when divided…

A:

Q: The area of a rectangle is (x^2 + 8x + 12) cm^2. If the length of the rectangle is (x+6) cm, show…

A:

Q: 4. If x=-4 and x=1 are the roots of x* + 3x' - 3x +3x – 4 = 0, find the other two roots of the…

A:

Q: Marcus states that the polynomial expression 3x3 – 4x2y + y3 + 2 is in standard form. Ariel states…

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Q: Show that (2x+7) is a factor 2x2+5x2-11x-14.Hence factories the given expression completly ,by using…

A:

Q: What does it mean to have a remainder of 0? This pertains to Division with Polynomials.

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Q: The polynomial -6x + 50x+ ax+ 24 has factors x-1 and 2x + 1. Determine the value of a.

A: Suppose px be the given polynomial such that px=-6x3+50x2+ax+24 And the factors of the polynomial…

Q: If the remainder on dividing the polynomial 2x* – kx +5x-3k+3 by (x + 2) is 4, then find the value…

A: Use the given information.

Q: What is the equation whose roots are reciprocal of the roots of the equation of 2x2 + 5x + 2 = 0?

A:

Q: Show that x2 − 4 is a factor of x4 − 5x3 + 2x2 + 20x − 24.

A:

Q: Prove that (x+2) is a factor of 3x'+8x+x-6 and find the other factor.

A: we have to find factor of the polinomial

Q: 27 comp 28. 8 comp 29. +9° +90 27 = x2-6x 28 = 3x2 - y 3-x2 - 13x + 9 Find mz8. What is the name of…

A: Complementary Angles:- Two angles are complementary if the sum of the measures of both the angles is…

Q: 12. If x=-1 is a root of x + 4x? -x -4 =0, use synthetic division to factor the polynomial…

A:

Q: One of the factor of kx^3+3x^2-2kx+1 is x+1. Find k

A:

Q: Find the coefficient of x11 in (x2 - 3x) / (1 - x )4

A: Solution:

Q: In the process of solving 2x3+7x2+9x+10=0, you test 1, 2, 5, and 10 as possible zeros and determine…

A: Given 2x3+7x2+9x+10

Q: Determine whether the statement makes sense or does not make sense, and explain yourreasoning: "When…

A: We have to determine whether the statement makes sense or does not make sense, and explain your…

Q: By what polynomial of lowest degree must (x2 – 64)(x² + 5x – 24) be multiplied to make it a perfect…

A: Givem polynomial is (x2-64)(x2+5x-24)To find lowest degree multiplier to make it perfect square.

Q: Show the proper algebraic steps to 2x+4 = 4x. %3D

A: According to the question, we have to solve the algebraic expression 2x+4=4x and find the value of…

Q: When using the FOIL method to find (x + 7)(3x + 5),the product of the first terms is_________ , the…

A: FOIL stands for First Outer Inner Last

Q: What is the result when 2x + 13x° + 17x2 - 10x 1 is divided by r(x) x + 3? If there is a remainder,…

A:

Q: For what value of a will five of the six real roots of 6x6 + 7x5 _ 43z4 - 153 + 49z2 + ax polynomial…

A: For what value of a will five of the six roots of polynomial P(x) be shared by the polynomial Q(x)

Q: If x=9 is a solution to a polynomial equation, then (x-9) will be a factor a that polynomial

A: The given statement is true.

Q: 5х-6 2x

A:

Q: 10) If x = 1 is a zero, what are the other zeros for x3 - 3x2 + x + 1 = 0 ?

A:

Q: Show that If 2 is a root of  kx4 - 11x3 + kx2 + 13x + 2 Then K = 3

A: Given,          2 is a root of kx4-11x3+kx2+13x+2 then k=3.

Q: 10) If x = -2 is a zero, what are the other zeros for 3x3 + 10x2 + 4x - 8 = 0? %3D

A:

Q: 8) If x = 2 is a zero, what are the other zeros for x3 – x2 - x- 2 = 0 ?

A:

Q: 7, 3x-10x3-17x + 48x + 36-D Zeros: Factors 8.2x-x-12x + 7x+ 16x-12 0 Zeros: Factors:

A:

Q: If the result of a polynomial division is 2x - 4x2- 5x + 23 make at least three definitive x+2…

A: Answer

Q: If x – 2 is a factor of x3- 4x2 + 8x + k then the value of k is

A: Given: x-2 is a factor of x3-4x2+8x+k.

Q: A polynomial f(x) = x³ + ax² – 3x + b when divided by 91 (x) = x – 2 gives a remainder of 6 and f(x)…

A: Given:             fx=x3+ax2-3x+b using remainder theorem: fx=x3+ax2-3x+b is divisible by g1x=x-2…

Q: In Example 2(a), can I simplify 5x 2(c), can I solve (x first step? = 20x by dividing both sides by…

A: When a single variable equation consists of terms on both sides containing the variable; then all…

Q: x2 - 4 is a factor of x4 - 5x3 + 2x2 + 20x - 24

A:

Q: 5. A friend was working on the problem: (10x³ + 18.x2 + 3x- 1) ÷ (5x + 4). 3 They got 2x² + 2x 1+ as…

A: From the exponents concept

Q: How can I show that there exists at least one solution in the set of real numbers for x5-x3+3x=5…

A:

Q: What is the product of x - 2x + 3 and x + 1? 1. x3- x2 + x + 3

A:

Q: Discuss the possibilities for the roots to : 2x'-5x - 6x+4 = 0 12. 3x - 5x -x² -8x+4 =0

A: We can use Descartes rule of signs to check the nature of possible roots of the given function, P(x)…

Q: To find the possible roots of the polynomial 4x3 + x4 - 7x² - 8x - 8

A:

Q: How can all real zeroes be found for 6x^3 - 24x^2 + 6x?

A: This question can be solved using the concept of finding the zeroes.