Let's solve this problem step-by-step.
First of all, let's establish that we are trying to obtain the factorised expression for:
2x^2 + 18
Now, there are two main ways we can solve this problem:
1 ) Expand and then simplify each of the options until one of them gives you the correct answer.
OR
2 ) Factorise the expression to give you one of the options as your answer.
I will be doing the first method today as although it is more time-consuming, it is easier to do as if you aren't able to directly factorise the expression you can use your expanding skills instead.
STEP-BY-STEP SOLUTION:
To begin with, we will expand and simplify each of the expressions to see which one gives us the correct answer as displayed below:
OPTION A -
= ( 2x - 9 ) ( x - 2 )
= 2x^2 - 4x - 9x + 18
= 2x^2 - 15x + 18
Therefore, Option A is incorrect.
OPTION B -
= ( 2x - 6 ) ( x - 3 )
= 2x^2 - 6x - 6x + 18
= 2x^2 - 12x + 18
Therefore, Option B is incorrect.
OPTION C -
= ( 2x - 6 ) ( x + 3 )
= 2x^2 + 6x - 6x - 18
= 2x^2 - 18
Therefore, Option C is incorrect.
OPTION D -
= ( 2x - 9 ) ( x + 2 )
= 2x^2 + 4x - 9x - 18
= 2x^2 - 5x - 18
Therefore, Option D is incorrect.
Hmmm, this is weird. I think that there is a mistake in either the question or answer options as all the options ended up being incorrect.
However, I believe it would be safest to pick the closest answer which would be Option C.
ANSWER:
Option C - ( 2x - 6 ) ( x + 3 )