Question

If x+1 and x-1 are factors of $a{x}^3+x^2-2x+b$, then the values of a and b are respectively

• A. 2, -1
• B. -1, 2
• C. 1, 2
• D. -1, -2

Answer 1

The correct option is A 2, -1

$f\left(x\right)=a{x}^3+x^2-2x+b$
(x+1) is factor of f(x).
$a+1-2+b\Rightarrow a+b=1$
$\Rightarrow a=1-b$ .........(1)
$\therefore$ (x-1) is a factor of f(x)
a-2 = 1 +b
$\Rightarrow a=3+b$ .........(2)
from (1) and (2), we get:
1 - b = 3 + b
$\Rightarrow -2b=2\Rightarrow b=\frac{2}{-2}$
$\therefore b=-1$
Substituting b=-1 in (1), we get
a = 1- b = 1- (-1)
$\therefore a=2$

So, the correct answer is option (a).