SOLUTION: Factoring Completely: How do you factor a problem like this: (x^2 + 10x + 21)

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Question 159231: Factoring Completely: How do you factor a problem like this: (x^2 + 10x + 21)

Answer by KnightOwlTutor(293) About Me  (Show Source):
You can put this solution on YOUR website!
Use the quadratic equation:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B10x%2B21+=+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=%2810%29%5E2-4%2A1%2A21=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+-3
x%5B2%5D+=+%28-%2810%29-sqrt%28+16+%29%29%2F2%5C1+=+-7

Quadratic expression 1x%5E2%2B10x%2B21 can be factored:
1x%5E2%2B10x%2B21+=+%28x--3%29%2A%28x--7%29
Again, the answer is: -3, -7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B10%2Ax%2B21+%29