1. P(x) = px' –8x² +qx +2 is divisible by 2x-1 and when divided by x-1, the remainder is 3, where p and q are constants. a. Find the values of p and q. b. Hence, using long division, factorize P(x) completely. c. Find all roots of P(x) if P(x)=0.

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Q: Find the remainder when x51 is divided by x + 4 in Z7[x].

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

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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 :…

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A: x=a is said to be a root of a polynomial f(x)=0 iff (x-a) is a factor of f(x).

Q: If x = -1 is a root of the polynomial 0 = x3 + 4x? + 2x – 1, what are the remaining roots? -3+V13 x…

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Q: 5 Calculate the roots of the following polynomial equations: (a) x³ – 6x² + 11x – 6 = 0 given x = 1…

A: Topic = Polynomials

Q: (b.) The function, f(x)= ax'-bx² +cx-12 , has a remainder 30 when divided by x - 3. If (x-2) and…

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Q: XII. Given two polynomials: A(x) = 12x3 - 4x2 - 3x +1 B(x) = (3x – 1)(5x – 2) – (9x² – 6x + 1) 1)…

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Q: Find the polynomial in x of the third degree, which vanishes when x=-1 and x=2 has  the value 8 when…

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Q: Approximate the roots of the polynomial f(x) = X3 - 7X + 6 using Bolzano method.

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Q: Use synthetic division to solve: Show your work for credit. x' - 4x* – 2x' + 4x? +x = 0 Hint: This…

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Q: f(x) = x + 9x² + 8x – 60 %3D

A: detailed solution is given below

Q: 5) Use long division to find the quotient Q(x) and remainder R(x). P(x) = 6x³ 2x² + 4x - 1 and d(x)…

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Q: Suppose Q is a polynomial of degree n>= 2 with distinct roots, none lying on the real axis.…

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Q: 1/2x2 + x − y − 2 = 0 Find the zeros if any

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Q: 3. Divide f(x)= x³ + 2x² - 2x+4 By (x-2) using synthetic division. What is the remainder?

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Q: Given that x = 2 is one root of g(x) = 2x* + 4x – 9x² – 11x – 6 = 0, use factorisation to determine…

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Q: Let P(x) be a polynomial of degree 5 with roots 2, – 5 and (3 + i). Write P(x) as a product of…

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Q: Let p(x)-x-5x?+4x-20. Verify that p(5)-0 and find the other roots of p(x)-D0.

A: p(x)= x3 - 5 x2 + 4x -20   Verify that p(5)=0; p(5)= 53- 5*52+4(5)-20 p(5)=0   Hence, x= 5 is one…

Q: For each polynomial the corresponding number k is a root of f(x). Use synthetic division to factor…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…