SOLUTION: Let p(x) = −x^4 + 3x^3 + 13x^2 − 15x.
(a) Find all zeros of p(x)
(b) Factor p(x) completely
(c) Sketch the graph of p(x) using a sign diagram
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-> SOLUTION: Let p(x) = −x^4 + 3x^3 + 13x^2 − 15x.
(a) Find all zeros of p(x)
(b) Factor p(x) completely
(c) Sketch the graph of p(x) using a sign diagram
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Question 1157549: Let p(x) = −x^4 + 3x^3 + 13x^2 − 15x.
(a) Find all zeros of p(x)
(b) Factor p(x) completely
(c) Sketch the graph of p(x) using a sign diagram Answer by Boreal(15235) (Show Source):
-3/ 1----- -3 ------ -13 ----- 15
shown to be 1 --- -6 ----- 5. which is x2-6x+5
so -3 is a root, and the trinomial factors into (x-5)(x-1)
roots are -3, 0, 1, and 5
factors are -x(x+3)(x-1)(x-5).
go back to -x^4+3x^3+13x^2-15x
when x becomes very negative, < -3. so does the function
-3 < x < 0 will be positive
0< X < 1 will be negative
1 < x < 5 will be positive
and for large + x >5 the function will be negative.
