Question

1.3x⁴ - 15x² + 12

Explanation:

Step1: Substitute $y=x^2$

Let $y = x^2$, then the polynomial becomes:
$3y^2 - 15y + 12$

Step2: Factor the quadratic in $y$

First factor out the GCF 3:
$3(y^2 - 5y + 4)$
Then factor the quadratic trinomial:
$3(y - 1)(y - 4)$

Step3: Substitute back $y=x^2$

Replace $y$ with $x^2$:
$3(x^2 - 1)(x^2 - 4)$

Step4: Factor difference of squares

Use $a^2 - b^2=(a-b)(a+b)$:
$3(x - 1)(x + 1)(x - 2)(x + 2)$

Answer:

$3(x - 1)(x + 1)(x - 2)(x + 2)$