Question

Find factors of the polynomial $p\left(x\right)=4x^3+x^2+5x+8$
[3 Marks]

Answer 1

Let us assume that atleast one of the zeroes is an integer. Product of the factors is equal to the constant term (+8). Possible roots are the factors of +8. Hence, possible factors are:
$\pm 1,\pm 2,\pm 4,\pm 8$. (1 Mark)

Trying -1, we get:
$p(-1)=4\times {(-1)}^3+{(-1)}^2+5\times (-1)+8$
$p(-1)=-4+1-5+8=0$
So, (x + 1) is a factor of the polynomial P(x). (1 Mark)

The quotient obtained when p(x) is divided by (x + 1) is the other factor.

So, the other factor is $4x^2-3x+8$. (1 Mark)