# How do you factor 3x^2+36x+105?

May 18, 2018

$3 \left(x + 5\right) \left(x + 7\right)$

#### Explanation:

$\text{take out a "color(blue)"common factor } 3$

$= 3 \left({x}^{2} + 12 x + 35\right)$

$\text{to factor the quadratic}$

$\text{the factors of + 35 which sum to + 12 are + 5 and + 7}$

$= 3 \left(x + 5\right) \left(x + 7\right)$

May 18, 2018

$3 \left(x + 5\right) \left(x + 7\right)$

#### Explanation:

A quadratic polynomial can be factored if it has zeroes: you can write

$a {x}^{2} + b x + c = a \left(x - {x}_{1}\right) \left(x - {x}_{2}\right)$

if ${x}_{1}$ and ${x}_{2}$ are solutions of the polynomial. So, let's see if our polynomial has solutions: the quadratic formula yields

${x}_{1 , 2} = \setminus \frac{- 36 \setminus \pm \setminus \sqrt{1296 - 1260}}{6} = \setminus \frac{- 36 \setminus \pm 6}{6}$

So,

${x}_{1} = \setminus \frac{- 36 + 6}{6} = - 5$

${x}_{2} = \setminus \frac{- 36 - 6}{6} = - 7$

Thus, $3 {x}^{2} + 36 x + 105 = 3 \left(x + 5\right) \left(x + 7\right)$