Question

question
factor completely over the integers.
$x^4 + 5x^2 - 14$

Explanation:

Step1: Substitute $u=x^2$

Let $u = x^2$, rewrite the polynomial:
$u^2 + 5u - 14$

Step2: Factor the quadratic in $u$

Find two integers that multiply to $-14$ and add to $5$ (7 and -2):
$(u + 7)(u - 2)$

Step3: Substitute back $u=x^2$

Replace $u$ with $x^2$:
$(x^2 + 7)(x^2 - 2)$

Step4: Factor difference of squares

Factor $x^2 - 2$ over integers? No, $2$ is not a perfect square. Keep as is.

Answer:

$(x^2 + 7)(x^2 - 2)$