SOLUTION: steps to factor 12a^2 + 84ab + 147b^2

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Question 205536This question is from textbook
: steps to factor 12a^2 + 84ab + 147b^2 This question is from textbook

Found 2 solutions by stanbon, Targetweek:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
12a^2 + 84ab + 147b^2
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A little trick:
If you graph this as 12x^2 + 84x + 147 you
will see that -7/2 is a root.
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That means 2x+7 is a factor.
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Your problem:
= (2a+7b)(6a+21b)
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Cheers,
Stan H.

Answer by Targetweek(62) About Me  (Show Source):
You can put this solution on YOUR website!
if the equation is
12a%5E2+%2B+84ab+%2B+147b%5E2
then the answer is...
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 12x%5E2%2B84x%2B147+=+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=%2884%29%5E2-4%2A12%2A147=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%2884%29%29%2F2%5C12.
Expression can be factored: 12x%5E2%2B84x%2B147+=+12%28x--3.5%29%2A%28x--3.5%29

Again, the answer is: -3.5, -3.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+12%2Ax%5E2%2B84%2Ax%2B147+%29