# How do you factor 54 + 27t + 3t^2?

May 28, 2015

$f \left(t\right) = 3 \left({t}^{2} + 9 t + 18\right) = 3 \left(t - p\right) \left(t - q\right)$

Find p and q by composing factor pairs of $18$: (1, 18);(2, 9);(3, 6).

$p = 3$ and $q = 6$.

$f \left(x\right) = 3 \left[\left(t + 3\right) \left(t + 6\right)\right]$

May 28, 2015

Answer: $3 {t}^{2} + 27 t + 54 = 3 \left(t + 3\right) \left(t + 6\right)$

Problem: Factor $54 + 27 t + 3 {t}^{2}$.

Rewrite the equation as $3 {t}^{2} + 27 t + 54$.

Factor out the GCF $3$.

$3 \left({t}^{2} + 9 t + 18\right)$

Factor $\left({t}^{2} + 9 t + 18\right)$ by determining two factors of $18$ that when added equal $9$.

The numbers $3$ and $6$ meet the requirement.

The factors for $3 {t}^{2} + 27 t + 54$ are $3 \left(t + 3\right) \left(t + 6\right)$.