Question

I need help with number 4 pleaseeeee thank you !

Answer 1

D) -2, 3

Explanation:

First, factor r^4-13r^2+36 to get (r^2-2)(r^2-9)

Which, in simple terms, is (r+2)(r-2)(r+3)(r-3).

You should now have (r+2)(r-2)(r+3)(r-3) over r^3 + r^2 - 6r

Now, factor r^3 + r^2 - 6r to get r(r-2)(r+3)

Your equation should look like this:
`((r+2)(r-2)(r+3)(r-3))/(r(r-2)(r+3))`

Now, cancel out equal operations that lie both above and below the fraction line. So r-2 cancels out r-2 and r+3 cancels out r+3.

You now have
`((r+2)(r-3))/(r)`

Subtract 2 from 2 to get zero and add 3 to -3 to get zero.

0 over any number is equal to zero, so the roots are -2 and 3.