Question

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

Answer 1

(i) Let $p\left(x\right)=3x^2+6x–24$ ….(i)
On putting x = 2 in Eq. (i) we get,
$P\left(2\right)=3(2{)}^2+6(2)–24$
$=3\times 4+12–24=12–12=0$
Therefore, x - 2 is a factor.

(ii) Let $p\left(x\right)=4x^2+x–2$ ….(ii)
On putting x = 2 in Eq. (ii) we get,
$P\left(2\right)=4(2{)}^2+2–2=4\times 4+0$
$=16\ne 0$
Hence, x – 2 is not a factor of p(x).