The product (x - 2)(x + 3) is positive if both factors are negative or if both factors are positive. Therefore, we can solve (x - 2)(x + 3) > 0 as follows:(x - 2 < 0 and x + 3 < 0) or (x - 2 > 0 and x + 3 > 0)(x < 2 and x < -3) or (x > 2 and x > -3)x < -3 or x > 2The solution set is (-∞, -3) ∪ (2, ∞). Use this type of analysis to solve each of the following. ((x + 4)/(x - 7)) > 0

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: What is the result when 4x - 11a - 24x2 + 19x – 12 is divided by T(x) 4? If there is a remainder,…

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Q: Solve the given problem using any miscellaneous of algebraic method -ldr

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Q: 10. Solve for x: x = Vx +7- 5 11. Factor completely: 6x2 – 2z – xz +12x | 12. Rationalize the…

A: Solve the following

Q: To divide x^3+5x^2-2x+8 by x-5 using synthetic division,the first step is to write

A: According to question we have to calculate x3+5x2-2x+8x-5 By synthetic division

Q: What is the result when x4 6x3 + 4x2 + 18x – 12 is divided by x-4? If there is a remainder, express…

A: We will use long division method to find the answer

Q: i have a question about the step by step of 0= -x2+4x-5 using the quadratic formula

A: Consider the quadratic equation, -x2+4x-5=0 To solve the given equation,…

Q: What is the result when 3x + 21x³ + 26x2 + 4x - 7 is divided by x2 + 5x 3? If there is a remainder,…

A:

Q: Suppose you were asked to solve the following two problems on a test. (a) Find the remainder when…

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Q: What is the value of k so that (x3 +4x 2+x + k)÷(x+2) give a remainder of 3?

A: To find the value of k so that x3+4x2+x+k÷(x+2) gives a remainder 3.

Q: What is the result when 3x + 10x2 - x-9 is divided by a + 1? If there is a r(x) remainder, express…

A: Let fx=3x3+10x2-x-9 and gx=x+1 To divide fx by gx, we first rearrange the terms of fx as follows:…

Q: If x - 2 is one of the factor of x^3 - 8, what is the other factor?

A:

Q: If 3x + ax +3x+2 leaves a remainder of 4 on division by (3x-1), find a. Example: x=3;x-5

A:

Q: What is the result when 3x+ 2x-15x2 + 10 is divided by x - 1? If | - there is a remainder, express…

A: Given that: 3x4+2x3-15x2+10 is divided by x-1

Q: x*+x²+ 6x + 5- x - (-8 + 5x² + x* – x) ÷ (x – 1) 8.

A:

Q: Find the General Solutions for x, and x,. x1 = -4x1 + 3x2 x, = -2x1+ X2

A: NOTE: Refresh your page if you can't see any equations. .

Q: (a) Factor (fx)=x^3-4x^2+x-4 into factors of the form (x-c), given that 4 is a zero. (b)…

A:

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: How can the Factor Theorem be used to determine if x - 1 is a factor of x3 - 2x2 - 11x + 12?

A: Given: the polynomial function fx=x3-2x2-11x+12.

Q: I. Find the value of k so that the remainder in each division problem is (a) 21. (2x³ + 3x² + kx-2)…

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Q: When a polynomial x4+x3-10x2-1 is divided by another polynomial, the quotient is x3-3x2+2x-8 and the…

A: See the details solution below

Q: Explain how to solve x2 + 6x + 8 = 0 using factoring and the zero-product principle.

A:

Q: The product two odd integers is even, whereas the product of an odd integer and an even integer is…

A: The product of two odd integers is odd. The product of an odd integer and an even integer is even.

Q: 5x^2 - x - 4 Factor completely Using ax^2 +bx+c form

A:

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: 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: What is the remainder when f(x)=x^3−22x^2−16x−161f(x)=x3−22x2−16x−161 is divided by (x−37)?

A:

Q: If [x² - 2x + a] = 0 has no solution, then find where [] represents the greatest integer).

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Q: The product of 2x³ + 3x² + 1 and 2x² + 4 in z5[x]/ is: 5x^2+ 5x +1 4x+1 O x^2+2 None

A:

Q: What is the result when x4 2x – 8x2 + 22x + 6 is divided by - x² – 6? If there is a remainder,…

A: Simplify: x4-2x3-8x2+22x+6x2-6

Q: This problem requires that you show all work. Factor the GCF out of each term: 24z – 4x² + 16x Hint:…

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Q: find the quotient and remainder 3x^3-12x^2-9x+2 over x+3

A: Given query is to find quotient and remaineder using synthetic division.

Q: What is the result when 16x + 4x° - 14x2 - 23x - 3 is divided by 4x2 1? If there is a remainder,…

A:

Q: Find all solutions for x in [0,2pi) 3cosx+4sinxcosx=0 (How do you factor this. . . lol)

A:

Q: Find the quotient and the remainder when  2x^4+3x^3+x+1 is divided by 3x^2+1 in Z5[x].

A: We have to find the quotient and remainder when 2x4+3x3+x+1 is divided by 3x2+1 in ℤ5x

Q: Solve this strictly by Factor Theorem.  3x3 + 7x2 + 2x - 4

A: use the definition of factor theorem .

Q: What is the result when 2x4 - 6x³ - 13x2 + 13x + 1 is divided by 2x 9? If there is a remainder,…

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Q: -0-8X -0.2620 -1S. 81481482e + 4.81481481se Solve for x,

A: Solution :-

Q: If 2x³ 2x² - 9x² + 4x 7 is divided by x - 3 to give a quotient of 3x - 5 and a remainder of -22,…

A:

Q: Solve for x 4x^(2/3) +5x^(1/3) -6=0

A:

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: The product of x* + x3 + 2x? and 2x² + 4x + 6 in z, [x]/ is:

A:

Q: why is x = 2k in this problem?

A: given set is {2, 4, 6, 8, 10}

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

A:

Q: 3. If the area of a rectangle is expressed as x* - 9y? then the product of the length and the width…

A:

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.