Question

Factor completely. If the polynomial cannot be factored say it is prime.

1) 15x^3 + 19x^2 + 6x

A) (3x^2 +2)(5x+3)
B) x(3x+2)(5x+3)
C) x^2(3x+2)(5x+3)
D) x(5x+2)(3x+3)
E) Prime

I chose E) Prime.

2) 2x^2 - 14x - 6x + 42

A) 2(x+7)(x+3)
B) (x+7)(2x-6)
C) 2(x-7)(x-3)
D) (x-7)(x-3)
E) Prime

I know that this is 2x^2 - 20 + 42 when you combine the 14x and 6x so I chose answer E) Prime but I am not sure for this one.

Answer 1

1. Why don't you expand A) and see what you get?

2.
2x^2 - 14x - 6x + 42
= 2x(x-7) - 6(x-7)
= (x-7)(2x-6)
= 2(x-7)(x-3)

Answer 2

Just like what Reiny said, just try and expand it yourself. See what you can find! :)