Q.15 Check whether g(x) is a factor of p(x) or not, where p(x)=8x² – 6x² –4x+3 and x 1 g(x)= 3 4 If both x- 2 and 2x – 1 are factors of px² +5x+r , show that p = r. Without actual division, prove that 2x* - 5x +2x² – x+2 is divisible by x - 3xr+2 < >

Q: 3. Given that f(x) = x³ + px? + qx – 3 is exactly divisible by (x – 1) and leaves a remainder of 3…

A:

Q: 3. Let p(x) = 6xª – 13x³ + 13x² – 2. - (a) Find q(x) such that p(x) = (2x – 1)q(x) using synthetic…

A:

Q: Consider the following. P(x) = x³ − 9x² + 27x − 27 Use the remainder theorem to determine which is a…

A:

Q: 4. Find the product of (x +8)(x- 3) (X)

A:

Q: For the polynomial below, 2 is a zero. h(x)=x'+4x+ 6x- 36 Express h (x) as a product of linear…

A:

Q: 1. Factor the following polynomials using the factor theorem. (a) x³-4x²+x+6 (b) x³+8x²+21x+18 (c)…

A:

Q: Given h(r)=−r6+12r^5−80r^4+492r^3−1611r^2+2160r−972 and 6i is a zero of h, answer the following…

A: As many parts are given , I will solve only the first 3 parts : We are given :…

Q: . Factor x12 -1 as a product of irreducible polynomials over Z.

A: Given: x12-1. We have to factor x12-1 as a product of irreducible polynomials over Z.

Q: Evaluate the following polynomials? 1.P(2)=x³–3x²–x+2 2.P(3)=2x³+2x²–4x+1 3.P(-2)=x³–8x²–2x+5

A: As per the policy we are solving first three subparts.   Please repost and specify which subparts…

Q: Test the polynomial x – 2x3 + 6x – 3 for irreducibility over Q.

A: We have to check whether the polynomial x4-2x3+6x-3 is irreducible over the set of rational numbers…

Q: (a) Show that r= 3 is a solution of 3z 15+ 17z + 3 = 0. (b) Hence name the theorem that allows us to…

A:

Q: Verify the factorization using the FOIL method. (x + 3y)(x – 7y) = x? – 7xy + 3xy – 21y² = x² – 4xy…

A: The given expression is: x+3yx-7y=x2-7xy+3xy-21y2⇒x+3yx-7y=x2-4xy-21y2    -1 Thus, we have:…

Q: Use synthetic division method to find the quotient of each the following. Show the solution on the…

A: 1. (x3-3x2+5x+3)÷(x-3) Using synthetic division, The quotient is q(x)=x2+5. The remainder is…

Q: consider two polynomials P(x) =6x+1 and Q(x)=4x2-3x+2 carry out the indicated operation and simplify…

A: Explanation of the solution is given below...

Q: Which polynomial is equal to (x + 1) divided by (x + 1)? А - х3 — х2 -х+1 В — х3 + х2 — х + 1 B x*.…

A: WE HAVE TO FIND ANSWER

Q: How do i find the ral seros of  a given polynomial and their corresponding multiplicities?…

A: We have to find the zeroes and their multiplicities.

Q: USE SYNTHETIC DIVISION 16 x4 17 x2 2x - 6 ÷ x – 2 -

A: Solving the problem by finding the results.

Q: (x+1) is a factor of x²+2x²+2x+1 Find the other factor.

A: is a factor of .To find other factor.

Q: Determine Q(x) when P(x)=x³-5x2-3x+2 is divided by x-1 and then expressed in the form Select one: O…

A:

Q: What is the factored form of (xt + x³ + x² + x)? A. x(x+1)( x² + 1) С. x(х- 1)(x2 + 1) B. (x+ 1)( x²…

A:

Q: The factors of the trinomial 3x² + kxy – 2y? if k = 5 are O (3x – y) and (3x + 2y) o (3x – y) and…

A: If we have a given a polynomial like, where a, b and c are coefficients of real numbers, then we…

Q: 2. Divide the following polynomials using long division, and indicate the quotient Q(z) and the…

A: We have to find

Q: Find m so that x– 5 is a factor of f (x)= 4x² – 21x² +mx–15.

A: Consider the given polynomial fx=4x3-21x2+mx-15

Q: Open with 1.9.1 Dividing Polynomials conmuer (Conthua Using the previous example, complete the…

A:

Q: If (x + 3) is a factor of x3 - 13x – 12, what are the other factors. A. (x- 6) and (x + 2) B. (x –…

A: Given data is : If x+3 is a factor of x3-13x-12 What are the other factors.

Q: 10 Verify that given factors of f(x) and write complete factorization of f(x). a) f(x) = 5x³ – 6x² –…

A:

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

A:

Q: if P4(z) = r- 4r-3z2 + 4 and ro = -1. what is the polynomial Q(z) knowing that: P(z) = (z - zo)Q(z)…

A:

Q: Is x+ 4 a factor of f(x) = x5 + 10x4 + 29x3 – 28x2 (Use Synthetic Division in conjunction with the…

A:

Q: 5. (x5 + 25x3 -7x2 +37x 18) + (*+5) %3D II. A. Use the REMAINDER THEOREM to find the remainder of…

A: We have to solve

Q: 7x 6 completely if (x 1) is a factor Factor

A: Given that (x+1) is a factor of x3-7x-6. Divide the polynomial x3-7x-6 by x+1 as follows.