Question

on dividing x^3-3x^2+x+2 by a polynomial g(x) the quotient and reminder were x-2-2x+4 respectively then find g(x).​

Answer 1

Answer:

g(x) = x² - x + 1

Step-by-step explanation:

On dividing x3-3x2+x+2 by a polynomial g(x),the quotient and remainder were x-2 and -2x+4 respectively.find g(x)

f(x) = x³ - 3x² + x + 2

q(x) = x - 2

let say

g(x) = ax² + bx + c

r = - 2x + 4

f(x) = g(x)q(x) + r

=> x³ - 3x² + x + 2 = (ax² + bx + c)(x - 2) + (-2x + 4)

=> x³ - 3x² + x + 2 = ax³ + x²(b - 2a) + x(c - 2b) -2c -2x + 4

=> x³ - 3x² + x + 2 = ax³ + x²(b - 2a) + x(c - 2b - 2) + (-2c + 4)

Equating Power terms

a = 1

b - 2a = - 3 => b -2 = -3 => b = -1

c - 2b - 2 = 1 => c + 2 - 2 = 1 => c = 1

or -2c + 4 = 2 => -2c = -2 => c = 1

g(x) = x² - x + 1

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Answer 2

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