Question

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

E Prime

Explanation:

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

Answer 2

1.
`15x^(3) + 19x^(2) + 6x`

`x(15x^(2)) + x(19x) + x(6)`

`x(15x^(2) + 19x + 6})`

`x(15x^(2) + 9x + 10x + 6)`

`x(3x(5x) + 3x(3) + 2(5x) + 2(3))`

`x(3x(5x + 3) + 2(5x + 3))`

`x(3x + 2)(5x + 3)`

`The\ answer\ is\ B.`

2.
`2x^(2) - 20x + 42`

`2(x^(2)) - 2(10x) + 2(21)`

`2(x^(2) - 10x + 21)`

`2(x^(2) - 7x - 3x + 21)`

`2(x(x) - x(7) - 3(x) + 3(7))`

`2(x(x - 7) - 3(x - 7))`

`2(x - 3)(x - 7)`

`The\ answer\ is\ C.`