How do you solve #3x^2-13x-10=0# by factoring?

1 Answer
Oct 10, 2015

Answer:

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

Explanation:

Because #3# can only have factors of #3# and# #1
you know those will be your coefficients for #x#.
That is your factors will be of the form
#color(white)("XXX") (3x +a)(x +b )#

You also know that one of #a# or #b# will have #+# and one side will have #-# due to the #color(red)(-)10#.

The options for #10# are
#2xx5# or #1x10#.

Using #2xx5#
if you multiply the #5# by #3# it gives you #15#
and the #2# by #1#1 you get #2#.

Because #13# in the center (of the original form) is negative
you know the #5# needs to be negative

and the factors are
#color(white)("XXX")(3x+2)(x-5)#