75/7×5 which choice is the most reasonable answer a 32 4/7 b 41 4/7 c 34 4/7 d 38 4/7

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 )