Question

What are the factors of 2x2 + 3x – 54? Check all that apply.

2x – 9
2x – 6
2x + 6
x + 9
x – 6
x + 6

Answer 1

2x^2 + 3x – 54 = (2x - 9) (x + 6), so A and F

Answer 2

ANSWER

The factors are

$(2x - 9) \: \: and \: \: (x + 6).$



EXPLANATION

The given expression is
$2 {x}^{2} + 3x - 54$

This is a quadratic trinomial.

We need to factor this by splitting the middle term.


We know that,
$a=2, b=3,c=-54$


So
$ac = - 108$

Two factors of -108 that sums up to 3 is
$12 \: and \: 9$


We now split the middle term to obtain,


$2 {x}^{2} + 3x - 54 = 2 {x}^{2} + 12x - 9x - 54$



We factor to obtain,

$2 {x}^{2} + 3x - 54 = 2x( x + 6) -9( x + 6)$
We factor further to obtain,

$2 {x}^{2} + 3x - 54 = ( x + 6) (2x-9)$


Hence the factors are
$(2x - 9) \: \: and \: \: (x + 6)$


The correct answers are option A and F