# How do you factor 3x^2 + 54x + 195?

Jan 30, 2016

3 (x + 5 )(x + 13 )

#### Explanation:

There is a common factor of 3 in all the terms .

hence 3 $\left({x}^{2} + 18 x + 65\right)$

now ${x}^{2} + 18 x + 65 \textcolor{b l a c k}{\text{ is a trinomial }}$

To factorise this : consider the factors of 65 which also sum to

give the coefficient 18 of the x term.

factors of 65 are : 1, 3, 5,13, 65

the pair then are 5 and 13 as they sum to give 18.

${x}^{2} + 18 x + 65 = \left(x + 5\right) \left(x + 13\right)$

Completing the factorisation : 3(x + 5 )(x + 13 )