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).`



Step-by-step 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