SOLUTION: I need help on factoring this polynomial: {{{ 8x^2+2x-21 }}}

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Question 872939: I need help on factoring this polynomial: +8x%5E2%2B2x-21+
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
+8x%5E2%2B2x-21+
8(x^2 + x/4 - 2.625)
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0.25x%2B-2.625+=+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=%280.25%29%5E2-4%2A1%2A-2.625=10.5625.

Discriminant d=10.5625 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0.25%2B-sqrt%28+10.5625+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280.25%29%2Bsqrt%28+10.5625+%29%29%2F2%5C1+=+1.5
x%5B2%5D+=+%28-%280.25%29-sqrt%28+10.5625+%29%29%2F2%5C1+=+-1.75

Quadratic expression 1x%5E2%2B0.25x%2B-2.625 can be factored:
1x%5E2%2B0.25x%2B-2.625+=+1%28x-1.5%29%2A%28x--1.75%29
Again, the answer is: 1.5, -1.75. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0.25%2Ax%2B-2.625+%29

8(x - 1.5)(x +1.75)