SOLUTION: Factor completely 8w^7+6w^6-20w^5

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Question 297228: Factor completely 8w^7+6w^6-20w^5
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
2 is the GCF of 8,6,and 20
w^5 is the GCF of w^7,w^6,w^5
so
2w%5E5%284w%5E2%2B3w-10%29 do quadratic formula
2w%5E5%284%28w-1.25%29%28w%2B2%29%29
8w%5E5%28w-1.25%29%28w%2B2%29%29 completely factored
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aw%5E2%2Bbw%2Bc=0 (in our case 4w%5E2%2B3w%2B-10+=+0) has the following solutons:

w%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=%283%29%5E2-4%2A4%2A-10=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+169+%29%29%2F2%5Ca.

w%5B1%5D+=+%28-%283%29%2Bsqrt%28+169+%29%29%2F2%5C4+=+1.25
w%5B2%5D+=+%28-%283%29-sqrt%28+169+%29%29%2F2%5C4+=+-2

Quadratic expression 4w%5E2%2B3w%2B-10 can be factored:
4w%5E2%2B3w%2B-10+=+4%28w-1.25%29%2A%28w--2%29
Again, the answer is: 1.25, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B3%2Ax%2B-10+%29