3) Determine the value of k such that when f(x) = x* – 3x+ kx² + 2 is divided by x – 2, the remainder is 2. 4) Factor fully. a) x³ + 4x² + x – 6 b) 2x³ – 9x² + 7x + 6

Q: 1.Solve the following polynomial equations.  a) 2X2+1=x2+2X b) x3+6x2+11x+6=0 C)x5-4x3-x2+4=0…

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Q: Is (x – 5) a factor of (2x – 9x² – 12x + 35) ? Justify your answer

A: Given equation is  2x3 -9x2-12x+35 Whether (x-5) s a factor or not?

Q: Create a cubic expression that when divided by (x-1) will have a remainder of 6

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Q: 1.Solve the following polynomial equations.  a)  2X2+1=x2+2X b)   x3+6x2+11x+6=0 C)…

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Q: What is the degree of the polynomial 3x4-5x3+7x2-2x+8?

A: Degree of polynomial: The highest or the largest power of the variable denotes degree of variable…

Q: 6) Suppose the cubic polynomial 8x³ + mx² + nx - 6 has both 2x + 3 and x - 1 as factors. Find m and…

A: Given polynomial equation:- 8x3+mx2+nx-6

Q: 14.) Factor each polynomial using the factor theorem. a) x - 5x2 - b) 2x3 + x2 - 27x- c) 3x 22x 16 -…

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Q: Find [(5x+3x²) da dx + C

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Q: 3. Verify x + 2 and x – 4 are factors of P(x) = 8x* – 14x³ – 71x² – 10x + 24. %3D

A: Explanation of the answer is as follows

Q: 6. Factor each polynomial using the factor theorem.1 3- 3x2. 10x + 24 d) 4x* + 7x e) x - 5x – 7x³ +…

A: We find out the factors of the given polynomials.

Q: 11) Use long division to divide (3x² – 14x – 5) by (x – 5). Is x – 5 a factor of 3x2 – 14x – 5?…

A: Given ( 3x2 - 14x -5) by (x-5)

Q: 20) Determine a polynomial that represents the area of the figure. 20) 3x - 5 3x + 5 A) 9x2 - 25 B)…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 10. Use synthetic division to divide. a. (4x + x2 – 11x + 6) + (x + 2) b. (24 + 5x + 22x – 27x2) +…

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Q: The value of r for which x2 - rx - 2 and x3 + x2 - x - 1 have a common factor is?

A: Given two equations x2-rx-2=0 and x3+x2-x-1=0

Q: For the remainder of the division of x-2x²+3kx+18 by x-6 to be equal to zero, k must be equal to?

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Q: 1.Solve the following polynomial equations.  a)  2X2+1=x2+2X b)   x3+6x2+11x+6=0 C)…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: 1. State the zeros of each by first rewriting the equation in factored form: a) y= x² - 6x – 16 b) y…

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

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Q: Factor.  A) x2-2x-35   B) x2+2x-35

A: A) We will factor -35 so that the sum of the factors= -2 Such factors are -7 and 5 So we write -2x…

Q: According to the Factor Theorem, which are zeros of f(x)=2x^3−22x^2+72x−72 given that (x−6) is a…

A: Given problem:- According to the Factor Theorem, which are zeros of f(x)=2x3 −22x2 +72x−72 given…

Q: 1.Solve the following polynomial equations.  a) 2X2+1=x2+2X b) x3+6x2+11x+6=0 C)x5-4x3-x2+4=0…

A: As per bartleby guideline for more than three sub parts asked only first three are to be answered…

Q: ind the quotient using polynomial long division. 23. (18x +6x +9) ÷ (3x – 2) 13 A) 6x-2+ B) 6x+6- 3x…

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Q: (A) x² +6x+k (B) x²-x+k (C) x² +19x+k

A: answer is in step2

Q: Find the product. Assume variables represent positive real numbers. 2) 2x2/5(x11/5-3x) A)2x13/5 -…

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