Question

factor the trinomial completely.
$x^4 - 5x^3 + 6x^2$

Explanation:

Step1: Factor out GCF

$x^4 - 5x^3 + 6x^2 = x^2(x^2 - 5x + 6)$

Step2: Factor quadratic trinomial

Find two numbers that multiply to $6$ and add to $-5$: $-2$ and $-3$.
$x^2 - 5x + 6 = (x - 2)(x - 3)$

Step3: Combine factors

Substitute factored quadratic back.

Answer:

$x^2(x - 2)(x - 3)$