Question

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)

Answer 1

Choice A is the answer.

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.

Answer 2

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

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)