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.

Q: 16) Given the function f(x)=2x –1lx² +22x–15, find all the complex roots, given that 2-i is a root.…

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Q: 4. If x=-4 and x=1 are the roots of x* + 3x' - 3x +3x – 4 = 0, find the other two roots of the…

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Q: Find the remainder when the polynomial 2x* – 5x³ + 12x – 7 is divided by (x – 1). A. 2 В. — 12 С. —…

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Q: D 20. Marco wants to show that x³-y - (x-y)x² +xy +y is true for all values of x and y. Marco makes…

A: The given identity is  x3-y3= (x-y)(x2+xy+y2)

Q: 1. Use synthetic division to find to find each quotient. Write your answer in the form of R(x) f(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: 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: 1. Which of the following is a polynomial? A. 5x 4x 1+7 B. xV5 + x? D. 3x5 – 5

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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: Given the polynomial: f (x) = 2x° + mx* – 40x° + nx² + 218x – 168 And that two of the roots are x= 1…

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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)-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: Use synthetic division to find the remaining zeros of each polyn 4. f(x) = x² − 6x³ + 20x² - 22x -…

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Q: - Express P(x) = xª +.2x³ + 2x² - x - 3 in terms of Legendre's polynomials

A: In this problem, we use Rodrigue's formula to express Legendre's polynomials.

Q: 3. Multiply: a. (5y + 4b) (5y- 4b) b. Suppose f(x = x - 5 and g(x) = 6x2 - 6x- 7. Then (fg)(x)=? %3D

A: According to the guidelines in case of multiple questions, We are only supposed to solve first…