Question

Factor the expression completely. (If the expression is not factorable using integers, enter PRIME.)
x4 − x2 − 42

Answer 1

(x^2 -7)(x^2 + 6)

Answer 2

Let's tell that \[x^2=t\]
then
\[x^4-x^2-42=t^2-t-42\]
let's find the roots of \[t^2-t-42=0\]
\[t_{1,2}=\frac{1\pm \sqrt{1+168}}{2}=\frac{1\pm 13}{2}=7;-6\]
so you can write\[t^2-t-42\]
as a factor:\[(t-7)(t+6)\]
Remind that \[t=x^2\]
put it in factor and you get:
\[(x^2-7)(x^2+6)\]