SOLUTION: I just learned this today and not sure how to do this. Please help. I have a quiz tomorrow on it. It is factoring. Thank you!! 4m^2+20m+24

Algebra ->  Exponents -> SOLUTION: I just learned this today and not sure how to do this. Please help. I have a quiz tomorrow on it. It is factoring. Thank you!! 4m^2+20m+24      Log On


   

Question 248453: I just learned this today and not sure how to do this. Please help. I have a quiz tomorrow on it. It is factoring. Thank you!!
4m^2+20m+24
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
factor out 4 first
4m^2+20m+24
4*(m^2+5m+6)
We are looking for factors of 6 that add up to 5
6,1 or 3,2
obviously 3,2
4(m+3)(m+2)
see another way to work out the equation
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B5x%2B6+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%285%29%5E2-4%2A1%2A6=1.

Discriminant d=1 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+1+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+1+%29%29%2F2%5C1+=+-2
x%5B2%5D+=+%28-%285%29-sqrt%28+1+%29%29%2F2%5C1+=+-3

Quadratic expression 1x%5E2%2B5x%2B6 can be factored:
1x%5E2%2B5x%2B6+=+1%28x--2%29%2A%28x--3%29
Again, the answer is: -2, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B6+%29