Question

If $2x^3-5x^2+x+2=(x-2)(a{x}^2-bx-1)$ , then $a$ and $b$ are respectively

• A. $2,1$
• B. $2,-1$
• C. $1,2$
• D. $-1,\frac{1}{2}$

Answer 1

The correct option is A $2,1$

$2x^3-5x^2+x+2=(x-2)(a{x}^2-bx-1)$

Using coefficient equating approach,

$⟹2x^3-5x^2+x+2=a{x}^3-2a{x}^2-b{x}^2-2bx-x+2$

$⟹2x^3-5x^2+x+2=a{x}^3-(b+2a)x^2+(2b-1)x+2$

Equating terms of both sides,

$a=2,2a+b=5,b=1$

$a=2,b=1$ Ans