SOLUTION: How do I find the 4 x- and single y-intercepts of this polynomial? {{{y=-x^4+13x^2-36}}} Thank you

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do I find the 4 x- and single y-intercepts of this polynomial? {{{y=-x^4+13x^2-36}}} Thank you      Log On


   

Question 908219: How do I find the 4 x- and single y-intercepts of this polynomial?
y=-x%5E4%2B13x%5E2-36
Thank you
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

y-intercept(when x = 0) is -36 

x-intercepts: -3,-2,2,3 can be found with Synthetic Division noticing x=2 is one root

2  -1	0	13	0	-36

	-2	-4	18	36

   -1	-2	9	18	0

(x-2)(-x^3 -2x^2 +9x + 18)  Note: x = -2 root for -x^3 -2x^2 +9x + 18

-2  -1	-2	9	18	

	2	0	-18	

   -1	0	9	0

(x-2)(x+2)(-x^2 + 9)

((x-2)(x+2)(x-3)(x+3)