Question

Determine which of the following polynomials has $x-2$, a factor :
(i) $3x^2+6x-24$
(ii) $4x^2+x-2$

• A. (i)
• B. (ii)
• C. Both A and B
• D. None of above

Answer 1

The correct option is A (i)

Let $g\left(x\right)=x-2$
Now,$g\left(x\right)=x-2$
$=>x-2=0$
$=>x=2$
(i)
Let $p\left(x\right)=3x^2+6x-24$
Now, $g\left(x\right)$ is a factor $p\left(x\right)$ if $p\left(2\right)=0$
Thus, $p\left(2\right)$
$=3(2{)}^2+6(2)-24$
$=12+12-24$
$=0$
Thus, $g\left(x\right)$ is a factor of $p\left(x\right)$
(ii)
Let $p\left(x\right)=4x^2+x-2$
Now, $g\left(x\right)$ is a factor $p\left(x\right)$ if $p\left(2\right)=0$
Thus, $p\left(2\right)$
$=4(2{)}^2+2-2$
$=16$
$\ne 0$
Thus, $g\left(x\right)$ is not a factor of $p\left(x\right)$
So, (i) is the factor of $x-2$