How do you factor completely #6x^2 + x - 15#?

1 Answer
Mar 11, 2016

Answer:

#6x^2+x-15=(3x+5)(2x-3)#

Explanation:

Use an AC method: Look for two factors of #AC = 6*15 = 90# which differ by #B=1#.

The pair #9, 10# works.

Then use that pair to split the middle term and factor by grouping:

#6x^2+x-15#

#=6x^2-9x+10x-15#

#=(6x^2-9x)+(10x-15)#

#=3x(2x-3)+5(2x-3)#

#=(3x+5)(2x-3)#