# How do you factor 3x^2 + 54x + 243?

Jun 14, 2015

$3 {x}^{2} + 54 x + 243 = 3 \left({x}^{2} + 18 x + 81\right) = 3 {\left(x + 9\right)}^{2}$

#### Explanation:

First separate the common scalar factor:

$3 {x}^{2} + 54 x + 243 = 3 \left({x}^{2} + 18 x + 81\right)$

The remaining quadratic factor is recognisable as a perfect square trinomial in that it is of the form ${a}^{2} + 2 a b + {b}^{2} = {\left(a + b\right)}^{2}$ with $a = x$ and $b = 9$.

Hence:

$3 \left({x}^{2} + 18 x + 81\right) = 3 {\left(x + 9\right)}^{2}$