How do you factor the expression #15x^3-23x^2+4x#?

1 Answer
Jan 17, 2017

Answer:

#15x^3-23x^2+4x = x(5x-1)(3x-4)#

Explanation:

Separate out the common factor #x#, then use an AC method...

#15x^3-23x^2+4x = x(15x^2-23x+4)#

To factor the quadratic, look for a pair of factors of #AC = 15*4 = 60# with sum #B=23#.

The pair #20, 3# works.

Use this pair to split the middle term and factor by grouping:

#15x^2-23x+4 = 15x^2-20x-3x+4#

#color(white)(15x^2-23x+4) = (15x^2-20x)-(3x-4)#

#color(white)(15x^2-23x+4) = 5x(3x-4)-1(3x-4)#

#color(white)(15x^2-23x+4) = (5x-1)(3x-4)#

Putting it all together:

#15x^3-23x^2+4x = x(5x-1)(3x-4)#