How do you factor #3x^2-11x-20#?

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Answer 1 · 2018-04-23T01:54:33

Find a factor multiplying to -60 (3*-20) and adds to -11

basically youll want to start by looking at the factors of -60 to see which will add to -11:

1 * 60
230
320
415
512
6*10
etc

As you can see, if you use the 4*15 factor, a negative 15 and a positive 4 will give you -11 if they're added and -60 when multiplied.

So you then replace the -11x with -15x + 4x to give you this:

#3x^2-15x+4x-20#

Then group them with parenthesis:

#(3x^2-15x)+(4x-20)#

Now find the GCFs of the things in the parenthesis:
You can factor a 3 and an x out of the first, and a 4 out of the second.

#3x(x-5) + 4(x-5)#

(you'll know if you did it right because the things still in parenthesis will be the same (the x-5))

Then the things on the outside of the parenthesis are put together as one factor and the ones inside are the other factor:

#(3x+4) and (x-5)# are the factors

(you can continue to solve it to find the values of x by setting the equations equal to 0)

#3x+4=0#

minus 4 on both sides
#3x=4#

divide both sides by 3
#x=4/3#

and
#x-5=0#

add 5 to both sides
#x=5#