SOLUTION: what is the factor of 10y^3+5y^2-15y I just can't get this one

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Question 405513: what is the factor of 10y^3+5y^2-15y
I just can't get this one
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
10y%5E3%2B5y%5E2-15y=5y%2A%282y%5E2%2By-3%29
Use method ax%5E2%2Bbx%2Bc=a%28x-x1%29%28x-x2%29, when x1, x2 - are the roots of the quadratic equations ax%5E2%2Bbx%2Bc=0
2y%5E2%2By-3=2%28y-y1%29%28y-y2%29
2y%5E2%2By-3=0
y=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
y=+%28-1+%2B-+sqrt%28+1%5E2-4%2A2%2A%28-3%29+%29%29%2F%282%2A2%29+
y1=+%28-1+%2Bsqrt%28+25+%29%29%2F4+ or y2=+%28-1+-sqrt%28+25+%29%29%2F4+
y1=1+ or y2=-1.5+
2y%5E2%2By-3=2%28y-1%29%28y-%28-1.5%29%29=2%28y-1%29%28y%2B1.5%29=%28y-1%29%282y%2B3%29
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10y%5E3%2B5y%5E2-15y=5y%2A%282y%5E2%2By-3%29=5y%28y-1%29%282y%2B3%29