how do you factor x^{2 }-9x-16,200
x^2 – 9x
-16,200
First, the
coefficient of the first term (1) is prime, so we will not be able to factor a
constant out. Next, there is no variable in the last term (16,200 (there is no
"x")), so we cannot factor out a variable.
Next, we
must find factors of 16,200 that differ by 9, so that when added together we
can get the -9 value that we need in the middle term.
Since
122*131=15,982 (which is less than 16,200), and 123*132=16,236 (which is greater than 16,200), these would be the possible factors of 16,200 that might have combined to produce the -9 that we were after. Since neither pair are actually factors of 16,200, it would seem that 16,200 does not have factors that differ exactly by a value of 9. Therefore, the polynomial cannot be factored. It must be prime.