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What are the factors of [tex]2x^2 + 3x - 54[/tex]? Check all that apply.

A. [tex]2x - 9[/tex]
B. [tex]2x - 6[/tex]
C. [tex]2x + 6[/tex]
D. [tex]x + 9[/tex]
E. [tex]x - 6[/tex]
F. [tex]x + 6[/tex]

Answer :

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

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ANSWER

The factors are

[tex](2x - 9) \: \: and \: \: (x + 6).[/tex]



EXPLANATION

The given expression is
[tex]2 {x}^{2} + 3x - 54[/tex]

This is a quadratic trinomial.

We need to factor this by splitting the middle term.


We know that,
[tex]a=2, b=3,c=-54[/tex]


So
[tex]ac = - 108[/tex]

Two factors of -108 that sums up to 3 is
[tex]12 \: and \: 9[/tex]


We now split the middle term to obtain,


[tex]2 {x}^{2} + 3x - 54 = 2 {x}^{2} + 12x - 9x - 54[/tex]



We factor to obtain,

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

[tex]2 {x}^{2} + 3x - 54 = ( x + 6) (2x-9)[/tex]


Hence the factors are
[tex](2x - 9) \: \: and \: \: (x + 6)[/tex]


The correct answers are option A and F