Question

if x^3 +x^2-2x-3=(x-2) (x2+ax+b)+5,then​

Answer 1

Answer:

a = 3   ,    b = 4         -------------- Ans

Step-by-step explanation:

x^3 + x^2 - 2x - 3    -------- where ^ represents raise to the power.

=> x^3 + x^2 - 2x -3 - 5 = (x-2)(x^2+ax+b)

=> x^3 + x^2 - 2x - 8 = (x-2)(x^2+ax+b)

At x = 2, x^3 + x^2 - 2x - 8 = 0

=> (x - 2) is a factor of x^3 + x^2 - 2x - 8;

Dividing x^3 + x^2 - 2x - 8 by (x-2), we get ---

(x-2)(x^2+3x+4) = (x-2)(x^2+ax+b)

=> x^2+3x+4 = x^2+ax+