Answer
$x^2(x - 5)(x + 1)$
Work Step by Step
Factor out the greatest common factor, which is $x^2$:
$x^2(x^2 - 4x - 5)$
The expression within parentheses is in quadratic form, which is $ax^2 + bx + c$.
Find factors that, when multiplied together, will equal $ac$, but when added together, will equal $b$.
In this expression, $a = 1$, $b = -4$ and $c = -5$; therefore, $ac = -5$.
Looking at the expression, one of the factors would have to be positive and the other negative, but the negative factor would have the greater absolute value. Let's look at the possibilities:
$-5$ and $1$
$5$ and $-1$
The first pair works/. Rewrite the expression in factor form:
$x^2(x - 5)(x + 1)$
Check the factorization with multiplication.
Expand the expression by multiplying the terms within them according to the FOIL method, meaning the first terms are multiplied first, then the outer, then the inner, and, finally, the last terms:
$=x^2[(x)(x) + (x)(1) + (-5)(x) + (-5)(1)]$
$=x^2(x^2 + x - 5x - 5)$
$=x^2(x^2 - 4x - 5)$
$=x^2(x^2) + (x^2)(-4x) + (x^2)(-5)$
$=x^4 - 4x^3 - 5x^2$
This is the same expression that we started out with. Therefore, the factoring is correct.
