How do you factor 10y3+20y2−6y?

1 Answer
marfre
Apr 11, 2018

2y(5y2+10y−3)=2y(y+1−2√105)(y+1+2√105)

Explanation:

Given: 10y3+20y2−6y

Find the greatest common factor (GCF) of each term:

10y3=2⋅5⋅y⋅y⋅y

20y2=2⋅2⋅5⋅y⋅y

−6y=−(2⋅3⋅y)

GCF is 2y

Factor the GCF: 2y(5y2+10y−3)

Factor the quadratic using the quadratic formula:

x=−B±√B2−4AC2A where Ax2+Bx+C=0

y=−10±√102−4⋅5⋅(−3)2⋅5=−1010±√16010

y=−1±√16√1010=−1±4√1010=−1±2√105

10y3+20y2−6y=2y(y+1−2√105)(y+1+2√105)

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