How do you factor 16n^2+ 43n -15?

May 31, 2016

$\left(16 n - 5\right) \left(n + 3\right)$

Explanation:

Any quadratic that can be factored can be expressed in the general form $\left(a x + b\right) \left(c x + d\right) = a c {x}^{2} + \left(a d + b d\right) x + b d$

We therefore need to find factors of $16$ and $- 15$ that in the right combination will give $43$

$16 = 16 \cdot 1$ and $15 = 5 \cdot 3$

$3 \cdot 16 = 48$

$48 - 5 \cdot 1 = 43$

$\therefore 16 {n}^{2} + 43 n - 15 = \left(16 n - 5\right) \left(n + 3\right)$