Question

Factor 10x2 – 42x – 108.

A)

2(10x – 9)(x + 6)

B)

(5x + 9)(x + 6)

C)

2(5x + 9)(x – 6)

D)

(x + 9)(5x – 6)

Answer 1

C

Explanation:

let's just think logically.

we have the expression

10x² - 42x - 108

so, we can rule out answers B and D, because we see that after doing the multiplication they will only create 5x² for the x² term (5x×x or x×5x).

and we can rule out A, because these multiplications will create 20x² for the x² term (2×10x×x).

that leaves us with C as correct answer.

to check :

2(5x + 9)(x - 6) = (10x + 18)(x - 6) =

= 10x² - 6×10x + 18x + 18×-6 =

= 10x² - 60x + 18x - 108 =

= 10x² - 42x - 108

correct

Answer 2

C. 2(5x + 9)(x - 6)

Explanation:

Let's go through each choice and see what is wrong and which is right.

Choice A: 2(10x - 9)(x + 6)

multiplying the 2 with the 10x^2 would give us 20x^2 which is not 10x^2, so A is incorrect

Choice B: (5x + 9)(x + 6)

multiply 5x by x gives us 5x^2 which is not 10x^2, B is incorrect as well

Choice C: 2(5x + 9)(x - 6)

multiplying 2 by 5x^2 gives us 10x^2, and -6(9) = -54(2) which is indeed -108, C is the correct option

Choice D: (x + 9)(5x - 6)

multiplying 5x by x gives us 5x^2 not 10x^2, thus D is incorrect