Question

How many complete factors are there in $4b^3-24b^2-28b$?

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

$4b^3-24b^2-28b$
Take $4b$ as common, we get
$=4b(b^2-6b-7)$
$=4b(b^2-7b+b-7)$ (replacing $-6b$ into $-7b+b$ to factorise easily)
$=4b\left(b\right(b-7)+1(b-7)$
So the completely factored result is $4b(b+1)(b-7)$
Therefore, there are $3$ complete factors in $4b^3-24b^2-28b$