How do you factor #6a^3+13a^2+5a#?

1 Answer
Jim G.
Jun 24, 2018

#a(2a+1)(3a+5)#

Explanation:

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

#=a(6a^2+13a+5)#

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

#"the factors of the product "6xx5=30#

#"which sum to "+13" are "+3" and "+10#

#"split the middle term using these factors"#

#6a^2+3a+10a+5larrcolor(blue)"factor by grouping"#

#=color(red)(3a)(2a+1)color(red)(+5)(2a+1)#

#"take out the "color(blue)"common factor "(2a+1)#

#=(2a+1)(color(red)(3a+5))#

#6a^3+13a^2+5a=a(2a+1)(3a+5)#

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