How do you factor #50r ^ { 2} + 5r - 120#?

1 Answer
Jim G.
Jun 19, 2018

#5(2r-3)(5r+8)#

Explanation:

#"take out a "color(blue)"common factor "5#

#=5(10r^2+r-24)#

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

#"the factors of the product "10xx-24=-240#

#"which sum to + 1 are - 15 and + 16"#

#"split the middle term using these factors"#

#10r^2-15r+16r-24larrcolor(blue)"factor by grouping"#

#=color(red)(5r)(2r-3)color(red)(+8)(2r-3)#

#"take out the "color(blue)"common factor "(2r-3)#

#=(2r-3)(color(red)(5r+8))#

#10r^2+5r-120=5(2r-3)(5r+8)#

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