P(x)x+ A x(x+ 1x + 1) B. x(1)(x + 1) Facto x'+x +x. C. x( x - 1x + 1) D. x(-1)(x + 1) 3. Which of the following is the factored formed of x'+3x - 10x-24? A. (x+ 4x-3)(x+ 2) B. (x-4)(x-3)(x-2) C. (x-4)(x-3)(x+ 2) D. (x+ 4)(x+3)(x-2) 4. Which of the following is a factor of 2x -5x+3? A. x-3 B. 2x+3 C.x -1 D. 3x +2 5. What are the factors of x - 2x-24? A. (x+ 4)(x-6) 8. (x-12)(x+ 1) C. (x-8(x +3) D. (x+ 12 x- 12)

Q: Which of the following is the correct complete factorization of x4 - 1?…

A: To find the complete factorization of x4-1. Solution: We know that, a2-b2=a+ba-b Factorizing the…

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: 1. Show whether the given polynomials 1+4x + x², 2+ 5x + 3x2, 3x 5x, and 3+ 15x - 8x spans p,.…

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Q: Find a QR-factorisation of 1 1 -1 1 | 1 1 1 1 0 -

A: The given question is solved below.

Q: - Use synthetic division to factor the polynomial x + 3x- 10x - 24 completely if 3 is a zero. AY

A:

Q: 2. If the result of a polynomial division is 2x³ – 4x² – 5x + 23 make at least three x + 2'…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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

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Q: If x+2a is a factor of x5-4a2x3+2x+2a+3  find a

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Q: 4.  Show that X2? −4 is a factor of x4− 5x3 +2x?2+20x−24.

A:

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: By factorising x3+1, show that (for suitable values of x) 1/(x2-x+1) = ∑∞n=0 (-1)n x3n+ ∑∞n=0 (-1)n…

A: The given question is solved below.

Q: We begin the process of factoring a polynomial by first factoring out the assuming that there is one…

A: Consider the given statement. Let's explain it by an example. Example. 3x2+6x Now, find the factor…

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

A:

Q: What is the completely factored form of xy – xn

A: Given : xy3 - x3y

Q: If x+2a is a factor of x5-4a2x3+2x+2a+3  Find a

A:

Q: 8-94 c and d

A: see 2nd and 3rd step.

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

A:

Q: Completly factorize x5 + 4x4 + 7x³ + 8x² + 4x + 2 in Q[x]. Justify that the found factors are…

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

A:

Q: Which of the following is the factored form of x^3 + 3x^2 – 10x – 24? * - O (x - 4)(x – 3)(x – 2) O…

A: Let f(x) = x3 + 3x2 - 10x - 24

Q: 9. Find the quotient and the remainder of x³ + 2x² – 1 divided by 3x2 +1 in Z7[x].

A: Note that for Z_7  Any number is equal to the remainder when it is divided by 7.

Q: Which of the following is the correct complete factorization of x4 - 1? (x-1)^{2}(x+1)^{2}

A: Given, x4-1

Q: 4. When the polynomial P(x) is divided by (x-2)2 the remainder is 3x - 3. What is the remainder when…

A:

Q: How do I factor the following- f(x)= (x+1) (x2-6x+5)

A: Given : f(x)= (x+1) (x2-6x+5)

Q: 1. Is (x – 3) a factor of the polynomial p(x) = x' – 11x + 6? Why or why not? 2. What is the…

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Q: (d) Show that x^2 − 4 is a factor of x^4 − 5x^3 + 2x^2 + 20x − 24.

A:

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: 1. Write the complete factored form of f(x). y 8. y = f(x) 4 -2 2 3 -8

A: Note  Factor form of a function is given by  f(x) =(x-a)(x-b)(x-c)....... and so on Where  a,b,c are…

Q: The polynomial 3x2 + bx - 4 has x - a as a factor, where a #0. Express b in terms of a.

A: Given polynomial is 3x2+bx-4...........(1) (x-a) is a factor of (1), so plugging x=a in the given…

Q: I. Use the Factor Theorem to determine whether the given binomial of the form x - c is a factor of…

A:

Q: Determine the completely factored form of fx) = x+ 3x -x- 3. c. Ax) = (x+ 3)*(x+ 2)(x+ 1) d. Ax) =…

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Q: b. Find a QR-factorisation of 1 -1 1 1 1 1 -1 0 |

A: Step:-1 Given matrix  is  110-1010111-10 Let  A= 110-1010111-10 Now, we'll apply Gram-Schmidt…

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

A:

Q: 29. Select the quadratic polynomial with roots –1 and 4. x2 + 3x – 4 x3 – 2x2 – 7x – 4 4x² + 8x + 4…

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Q: Which polynomials have been factored correctly? Ox+ 9x*+ 8x - 60 (x+ 5)(x- 2)(x+ 6) 3 120x'+ 164x*+…

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Q: 22. Find the quotient and the remainder for each of the followir x3-4x2+2x+5 1) x-2 4x3-2x2-3 2)…

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Q: 1. Which polynomial has 31, -31, and 3 (with multiplicity 2) as its roots? A -3x' +9x + 27 Bx -6x'…

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Q: By what polynomial must x3-4 x2y+5xy2-2y3 be divided to obtain a quotient of x-y?

A:

Q: 2. If the result of a polynomial division is 2x3 – 4x? – 5x + 23 ,make at least three x+ 2…

A: The given result of a polynomial division is 2x3-4x2-5x+23x+2. Observe the following. Quotient,…

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: 5. If the remainder dividing the polynomial P(x) = 2x³ + kx? + 7x +6 by x- 4 is 114, find the…

A: Quotient Remainder theorem  The answer after we divide one number by another. dividend ÷ divisor =…

Q: Show that x-1 is a factor of P(x)=x² − 6x² +11x-6 and hence, determine all factors.

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

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Q: 15) Find the remainder of the polynomial 5x4 – 3x3 + 9x – 1 when divided by x + 3

A: