Q. 458

In the following exercises, factor completely.

$3 x^{3} - 36 x^{2} + 108 x$

Verified

Answer

On factoring, we get $3 x {(x - 6)}^{2}$ .

1Step 1. Given information.

Consider the given question,

$3 x^{3} - 36 x^{2} + 108 x$

Factor out the GCF,

$= 3 x (x^{2} - 12 x + 36)$

On simplifying the expression,

$= 3 x (x^{2} - 6 x - 6 x + 36) = 3 x {x (x - 6) - 6 (x - 6)} = 3 x {(x - 6)}^{2}$

2Step 2. Check the answers.

Check by multiplying,

= 3 x {(x - 6)}^{2} = 3 x (x^{2} + 36 - 12 x) = 3 x^{3} + 108 x - 36 x^{2}