Question

question
factor completely over the integers.
$x^4 + 13x^2 + 40$

Explanation:

Step1: Substitute $y=x^2$

Let $y = x^2$, rewrite the polynomial:
$y^2 + 13y + 40$

Step2: Factor the quadratic in $y$

Find two integers that multiply to 40 and add to 13 (8 and 5):
$(y + 5)(y + 8)$

Step3: Substitute back $y=x^2$

Replace $y$ with $x^2$:
$(x^2 + 5)(x^2 + 8)$

Answer:

$(x^2 + 5)(x^2 + 8)$