SOLUTION: Let g(x) = {{{ - x^4 + 13x^2 - 36}}} what are the four x-intercepts and the single intercept? Is the function g is (increasing or decreasing)

Algebra ->  Functions -> SOLUTION: Let g(x) = {{{ - x^4 + 13x^2 - 36}}} what are the four x-intercepts and the single intercept? Is the function g is (increasing or decreasing)       Log On


   

Question 909606: Let g(x) = +++++++++-++++++++x%5E4+%2B+13x%5E2++++++-++++++++36
what are the four x-intercepts and the single intercept?
Is the function g is (increasing or decreasing) on the interval (−∞, −6).

It is (increasing or decreasing) on the interval (6, ∞).

please explain how to solve. Thank you
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

g(x)    =   -++x%5E4+%2B+13x%5E2+-36

how to solve

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

Find x-intercetps:  -3,-2,2,3

I. By factoring (x^2 - 4)(x^2 -9) = (x-2)(x+2)(x-3)(x+3)

0r

II. By 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)

Or

III. by Graphing