factor 2m^2+27m+70

To factor the quadratic expression 2m^2 + 27m + 70, we need to find two binomial factors.

First, multiply the coefficient of the quadratic term (2) and the constant term (70). The result is 2 * 70 = 140.

Next, we need to find two numbers that multiply to give 140 and add up to the coefficient of the linear term (27 in this case). After examining the factors of 140, we find that 10 and 14 satisfy this condition since 10 * 14 = 140 and 10 + 14 = 27.

Now we rewrite the middle term of the quadratic: 27m = 10m + 14m.

We can then split the middle term using these new terms:

2m^2 + 10m + 14m + 70

Now, we group the terms in pairs and factor out a common term from each pair:

(2m^2 + 10m) + (14m + 70)

Factoring out the greatest common factor from each pair:
2m(m + 5) + 14(m + 5)

Now, we can see that (m + 5) is a common binomial factor in each term:

(2m + 14)(m + 5)

So the factored form of 2m^2 + 27m + 70 is (2m + 14)(m + 5).