Question

Factor 4m^2 +16m+15

Answer 1

Split the second term in 4m^2 + 16m + 15 into two terms

4m^2 + 10m + 6m + 15

Factor out the common terms in the first two terms, then in the last two terms

2m(2m + 5) + 3(2m + 5)

Factor out the common term 2m + 5

(2m + 5)(2m + 3)

Answer 2

(2m + 5)(2m + 3) is the fully factored form of the trinomial.

4m^2 + 16m + 15

With the way the trinomial is, we cannot factor it in it's current state.

We must check to see if splitting the middle term is possible.

List factors of 60

1 * 60

-1 * -60

2 * 30

-2 * -30

3 * 20

-3 * -20

4 * 15

-4 * -15

5 * 12

-5 * -12

6 * 10 (this digits satisfy the criteria for splitting the middle term.)

Split the middle term.

4m^2 + 6m + 10m + 15

Group the polynomials in terms of 2.

(4m^2 + 6m) + (10m + 15)

Factor each binomial.

2m(2m + 3) + 5(2m + 3)

Rearrange the binomials.

(2m + 5)(2m + 3)