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 $Ax^2 + Bx +C = 0$

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

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

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

How do you factor 10y^3 + 20y^2 - 6y10y^3 + 20y^2 - 6y?