# How do you factor a perfect square trinomial  16x^2 − 24x − 9?

Jun 14, 2015

This trinomial can't be factored

#### Explanation:

D = b^2 - 4ac = 576 + 576 = 1152 is not a perfect square. Therefor, this trinomial can't be factored.

Jun 14, 2015

$16 {x}^{2} - 24 x - 9$ is not a perfect square trinomial. The sign of the constant term is wrong.

$16 {x}^{2} - 24 x - 9 = \left(4 x - 3 + 3 \sqrt{2}\right) \left(4 x - 3 - 3 \sqrt{2}\right)$

#### Explanation:

Perfect square trinomials are of the form:

${a}^{2} \pm 2 a b + {b}^{2} = {\left(a \pm b\right)}^{2}$

It is still possible to factor $16 {x}^{2} - 24 x - 9$

$16 {x}^{2} - 24 x - 9 = \left(4 x - 3 + 3 \sqrt{2}\right) \left(4 x - 3 - 3 \sqrt{2}\right)$