# How do you factor completely 77x^2+102x+16?

Jan 5, 2016

$\left(11 x + 2\right) \left(7 x + 8\right)$

#### Explanation:

If the factored form of a quadratic is $y = \left(a x + b\right) \left(c x + d\right)$
the standard form is $a c {x}^{2} + \left(a d + b c\right) x + b d$
In this example therefore we need to find factors of $77 \left(a c\right)$ and $16 \left(b d\right)$ that add to give $102 \left(a d + b c\right)$
$77 = 7 \cdot 11$ and $16 = 8 \cdot 2$
$11 \cdot 8 + 7 \cdot 2 = 88 + 14 = 102$
The result is therefore $\left(11 x + 2\right) \left(7 x + 8\right)$