Hello, brendaursula!
I was asked to factor \(\displaystyle 18\,+\,7x^2\,-\,x^4\) and I factored it to \(\displaystyle (x^2\,+\,2)(x^2\,-\,9)\)
What did i do wrong?
Two things . . .
(1) If you multiply out your answer, you get: \(\displaystyle \,x^4\,-\,7x^2\,-\,18\)
\(\displaystyle \;\;\;\)which is
not what they gave you.
(2) \(\displaystyle x^2\,-\,9\) can be factored, so you aren't finished yet.
I suspect you factored by taking out a -1 first: \(\displaystyle \;-1(x^4\,-\,7x^2\,-\,18)\)
Then we get: \(\displaystyle \:-1(x^2\,+\,2)(x^2\,-\,9)\)
Replace the\(\displaystyle \,-1:\;\;(x^2\,+\,2)(\underbrace{9\,-\,x^2})\)
. . . . . . . . . . . . . . . . . . . . diff. of squares
. . . . . Answer: \(\displaystyle \
x^2\,+\,2)\overbrace{(3\,-\,x)(3\,+\,x)}\)