How do you factor 2m^2+ 11m + 5?

1 Answer
Apr 13, 2018

m=-5,-1/2

Explanation:

We know that one set of parentheses will be
(2m+a)

and the other will have to be
(m+b)

(Note: a and b are not the values from the equation, they are placeholders while solving)

So far we have:
(2m+a)(m+b)=0

Now let's find a and b

We know that a*b=5* because when you FOIL they have to multiply to equal 5. Therefore, we know that one of them equals 5 and the other equals 1 because 5 is prime so those are its only factors.

We also know that 2m*b+a*m = 11m. This can only be true if b=5 and a=1. Now that we have found our values, let's solve for m.

(2m+1)(m+5)=0

Let's examine the first set of parentheses. We know that

(2m+1)=0

Subtract 1 from each side

2m=-1

Now divide each side by 2

m=-1/2

Now, let's examine the second set of parentheses. We know that

(m+5)=0

Subtract 5 from each side

m=-5

Final answer:

m=-5,-1/2