Question

1. Factor this quadratic function:2x2 + 12x +16

Answer 1

`2(x+4)(x+2)`

Explanation:

We can start with the observation that every coefficent in the quadratic
`2x^2 + 12x +16` is a multiple of 2. Factoring out the 2, our expression becomes
`2(x^2+6x+8)`. Let's focus on the second term,
`x^2+6x+8`. To factor this, we want to find two numbers that multiply to 8 and add to 6. 4 · 2 = 8 and 4 + 2 = 6, so we can use that fact to split the middle term and factor the quadratic completely:

`x^2+6x+8\\=x^2+2x+4x+8\\=x(x+2)+4(x+2)\\=(x+4)(x+2)`

Putting that back with the 2 we factored out earlier, our fully factored function is

`2(x+4)(x+2)`

Answer 2

4 (3x + 5)

Explanation:

Simplify

4 + 12x +16

Simplify

12x + 20

Factor

4 (3x + 5)