How do you factor #y= x^2 – 3x – 40# ?

1 Answer
Mar 23, 2018

Answer:

It factors to (x+5)(x-8)

Explanation:

Because we see that the highest order of #x# is 2, and the #x^2# term has no constants, we can write the factored equation as such:

#(x+a)(x+b)=x^2+x(a+b)+(axxb)#

using those relationships:

#a+b=-3#
#axxb=-40#

Because the product of #a# and #b# is negative, we know that only one of those terms is negative. The next step is to figure out what combination gives that product and that sum.

I guessed that the numbers must be 5 and -8 because:

#5+(-8)=-3# <-- equation satisfied
#5xx-8=-40# <-- equation satisfied

Now that we have our factors, we can finish our factoring:

#(x+5)(x-8)#