How do you factor #3x^2-11x-20#?
1 Answer
Find a factor multiplying to -60 (3*-20) and adds to -11
Explanation:
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:
Then group them with parenthesis:
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.
(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:
(you can continue to solve it to find the values of x by setting the equations equal to 0)
minus 4 on both sides
divide both sides by 3
and
add 5 to both sides