Factor completely 2x2 + 28x + 96.

A) 2 (x + 6) (x + 8)

B) (2x + 12) (x + 8)

C) 2 (x + 4) (x + 12)

D) (2x + 4) (x + 12)

A) 2 (x + 6) (x + 8)

Step-by-step explanation:

2x2 + 28x + 96.

We first factor out 2

We get; 2 (x² + 14 + 48)

The we factor the expression x² + 14 + 48

Product = 48, sum = 14, numbers = 8 and 6

Therefore;

x² + 8x + 6x + 48

x (x+8) + 6 (x+8)

Thus; x² + 14 + 48 = (x+6) (x+8)

Hence, the factorized expression will be;

= 2 (x + 6) (x + 8)

Choice A is the answer.

Step-by-step explanation:

We have given a quadratic expression.

2x² + 28x + 96

We have to find factors of above expression.

Taking 2 common from given expression, we have

2 (x²+14x+48)

Splitting the middle term of the above expression so that the sum of two terms must be 14 and their product be 48.

2 (x²+8x+6x+48)

Making groups, we have

2 (x (x+8) + 6 (x+8))

Taking x+8 common from above expression, we have

2 (x+8) (x+6) which is the answer.