Answer:
[tex]2(x+4)(x+2)[/tex]
Step-by-step explanation:
We can start with the observation that every coefficent in the quadratic [tex]2x^2 + 12x +16[/tex] is a multiple of 2. Factoring out the 2, our expression becomes [tex]2(x^2+6x+8)[/tex]. Let's focus on the second term, [tex]x^2+6x+8[/tex]. 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:
[tex]x^2+6x+8\\=x^2+2x+4x+8\\=x(x+2)+4(x+2)\\=(x+4)(x+2)[/tex]
Putting that back with the 2 we factored out earlier, our fully factored function is
[tex]2(x+4)(x+2)[/tex]
