Question

factor $x^{4}+14x^{2}+49$ completely. all factors in your answer should have integer coefficients.

Explanation:

Step1: Substitute $u=x^2$

Let $u = x^2$, rewrite the expression:
$u^2 + 14u + 49$

Step2: Factor the quadratic

Recognize as perfect square trinomial:
$u^2 + 14u + 49 = (u + 7)^2$

Step3: Substitute back $u=x^2$

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

Answer:

$(x^2 + 7)^2$