How do you factor #4x^3 - 19x^2 - 5x#?

1 Answer
Jim G.
May 25, 2018

#x(x-5)(4x+1)#

Explanation:

#"take out a "color(blue)"common factor "x#

#=x(4x^2-19x-5)#

#"factor the quadratic using the a-c method"#

#"the factors of the product "4xx-5=-20#

#"which sum to - 19 are - 20 and + 1"#

#"split the middle term using these factors"#

#4x^2-20x+x-5larrcolor(blue)"factor by grouping"#

#=color(red)(4x)(x-5)color(red)(+1)(x-5)#

#"take out the "color(blue)"common factor "(x-5)#

#=(x-5)(color(red)(4x+1))#

#4x^3-19x^2-5x=x(x-5)(4x+1)#

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