Question

The polynomial $2x^3+13x^2+x-70$ is exactly divisible by $x-2$.

• A. Yes
• B. No
• C. Can not be determine
• D. Ambiguous

Answer 1

The correct option is A Yes

Given polynomial: $p\left(x\right)=2x^3+13x^2+x-70$.

To check: is $x-2$ is a factor of $p\left(x\right)$?

Equate $x-2$ to zero

$⟹x-2=0$

$⟹x=2$
Now $p\left(2\right)=2(2{)}^3+13(2{)}^2+2-70$
$⟹p\left(2\right)=16+52+2-70$

$⟹p\left(2\right)=0$
$⟹x-2$ is a factor of $p\left(x\right)$ $[\because p(2)=0]$

$\therefore p\left(x\right)=2x^3+13x^2+x-70$ is divisible by $x-2$