How do you factor 3x^4+15x^2-72?

1 Answer
Jun 17, 2016

$3 \left({x}^{2} - 3\right) \left({x}^{2} + 8\right)$

Explanation:

Call x^2 = X, and factor the trinomial in parentheses.
$f \left(x\right) = 3 \left({X}^{2} + 5 X - 24\right) .$
Find 2 numbers knowing sum (b = 5) and product (c = -24).
They are: -3 and 8.
$f \left(x\right) = 3 \left(X - 3\right) \left(X + 8\right) = 3 \left({x}^{2} - 3\right) \left({x}^{2} + 8\right)$