Question

On dividing x3+x2+x+1 by a polynomial g(x) the quotient and the remainder are x+1 and 2 (x+1) respectively find g (x)

Answer 1

Answer:

g(x) = x - 1

Step-by-step explanation:

p(x) = x³ + x² + x - 2

g(x) = ?

quotient = x² + 2x + 1

reminder = 2x - 1

divident = divisor × quotient + reminder

(x³ + x² + x - 2) = g(x) × (x²+2x+1)+(2x - 1)

(x³+x²+x-2) -(2x-1) = g(x) × (x² + 2x + 1)

x³ + x² + x - 2 - 2x + 1 = g(x)×(x² + 2x + 1)

x³ + x² - x -1 = g(x) × (x² + 2x + 1)

(x³ + x² - x - 1) / (x² + 2x + 1) = g(x)

x² + 2x + 1 | x³ + x² - x - 1 | x - 1

x³ + 2x² + x

-x² - 2x - 1

-x² - 2x - 1

0

g(x) = x - 1