How do you factor the expression #3x^2+13x-30#?

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Answer 1 · 2016-02-29T06:11:15

#3x^2+13x-30=color(blue)((x+6)(3x-5))#

#3x^2+13x-30# is a quadratic equation in the form #ax^2+bx+c#, where #a=3, b=13, c=-30#.

Use the AC Method

Multiply #axxc#.

#3xx-30=-90"#

Find two numbers that when added equal #13# and when multiplied equal #-90#. The numbers #18# and #-5# meet the requirements.

Rewrite the trinomial, replacing #13x# with #18x# and #-5x#.

#3x^2+18x-5x-30#

Separate the terms into two pairs of terms.

#(3x^2+18)-(5x-30)#

Factor out the GCF from each pair of terms.

#3x(x+6)-5(x+6)#

Factor out #(x+6)#.

#(x+6)(3x-5)#