How do you factor #10y^3 + 20y^2 - 6y#?

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Answer 1 · 2018-04-11T05:23:45

#2y(5y^2 + 10y - 3) = 2y( y +1 - (2sqrt(10))/5)(y +1 + (2sqrt(10))/5)#

Given: #10y^3 + 20 y^2 - 6y#

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

#10y^3 = color(red)(2) * 5 * color(red)(y) * y * y#

#20y^2 = color(red)(2) * 2 * 5 * color(red)(y) * y#

#-6y = -(color(red)(2) * 3* color(red)(y))#

GCF is #color(red)(2y)#

Factor the GCF: #2y(5y^2 + 10y - 3)#

Factor the quadratic using the quadratic formula:

#x = (-B+- sqrt(B^2 - 4AC))/(2A)# where #Ax^2 + Bx +C = 0#

#y = (-10+- sqrt(10^2 - 4*5*(-3)))/(2*5) = -10/10 +-sqrt(160)/10#

#y = -1 +- (sqrt (16)sqrt(10))/10 = -1 +- (4 sqrt(10))/10 = -1 +- (2 sqrt(10))/5#

#10y^3 + 20 y^2 - 6y = 2y( y +1 - (2sqrt(10))/5)(y +1 + (2sqrt(10))/5)#