#1**+2 **

3) 36x^3 + 96x^2 + 42x + 112

Take out the GCF between 36x^3 and 96x^2 = 12x^2

Take out the GCF between 42x and 112 = 14

So we have

12x^2 ( 3x + 8) + 14 (3x + 8) ..... (3x + 8) is common...so....

(3x + 8) (12x^2 + 14) ....note that we can factor a 2 out of the second factor...and we have...

(3x + 8)* 2* (6x^2 + 7) =

2(3x + 8) (6x^2 + 7)

4) 42n^3 - 48n^2 - 336n + 384

Take out the GCF between 42n^3 and 48n^2 = 6n^2

Take out the GCF between 336n and 384 = 48

So we have

6n^2 ( 7n - 8) - 48(7n -8)

(7n -8) (6n^2 - 48) ...and we can factor a 6 out of the second factor

(7n - 8) * 6 * ( n^2 - 8)

6(7n - 8) (n^2 - 8)

CPhill Sep 5, 2018