Question

If
x3 + x²-2x-3=(x-2) (x²+ax+b)+5
then find the values of a and b using
the concept of equality of polynomials).​

Answer 1

Step-by-step explanation:

x³ + x²-2x-3=(x-2) (x²+ax+b)+5

x³ + x²-2x-3=x³+ax²+bx-2x²-2ax-2b+5

x³-x³+x²+2x²-2x-3-5 = ax²+bx-2ax-2b

3x²-2x-8 = ax²-2ax+bx-2b

(3x²-2x-8) = ax²-2ax+bx-2b

(3x²-2x-8) = ax(x-2)+b(x-2)

(3x²-2x-8) = (ax+b)(x-2)

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

(3x+4) = (ax+b)

therefore a=3 and b=4