Suppose we have the expression [tex]6m^2+7m-5[/tex]. How do you factor it?
When we have a quadratic equation ax² + bx + c, we want to find two numbers that mulitply to equal ac and add to equal b.
In this case, we want to find two numbers that multiply to equal -30 and add to equal 7. Think about the factors of -30. We're going to need one negative number and one positive to multiply and get a negative one.
In this case, they are 10 and -3.
Now we must split the middle of the equation like this:
[tex]6m^2+10m-3m-5[/tex]
Now we factor.
[tex]2m(3m+5)-1(3m+5)[/tex]
[tex]\boxed{(2m-1)(3m+5)}[/tex]
The answer is D. 3m+5.
