Question

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

Answer 1

3 (x + 5 )(x + 13 )

Explanation:

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

hence 3 `(x^2 + 18 x + 65 )`

now `x^2 + 18x + 65 color(black)( " 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 + 18x +65 = (x + 5 )(x + 13 )`

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