Algebra 1, semester 2; ! what are the zeros of the function? f(x)=2x^2+16x+30

If you're asking questions like this, it generally means you have been given at least one tool for answering questions of this sort. Usually, that tool is the "quadratic formula." Factoring is another tool that is useful.

Here, you can factor this by first noticing that all coefficients are even, so a factor of 2 can be removed.

... f(x) = 2(x² +8x +15)

Since you're familiar with multiplying binomials, you know that

... (x +p)(x +q) = x² + (p+q)x +pq

Comparing coefficients, we see

... pq = 15

... p+q = 8

Now, 15 can be factored as 1×15 or 3×5. The latter two factors sum to 8, so we could choose p=3, q=5, and our factorization of f(x) can be

... f(x) = 2(x +3)(x +5)

Finding the zeros means finding the values of x that make f(x) = 0. That is, we want x such that

... 2(x +3)(x +5) = 0

We know that either factor being zero will make the product zero, so the zeros are ...

... x = -3 or x = -5

answer: it is a.,b.,d.

step-by-step explanation: