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

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): You can put this solution on YOUR website!
factor out a -x(x^3-3x^2-13x)+15)=0
x=0
synthetic division using -3

-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.

RELATED QUESTIONS
Let p(x) = x^6 - 3x^4 + 2x^2 (a) Factor p completely. (b) Find the real zeros of p.... (answered by josgarithmetic,ikleyn)

1. Let p(x) = x^3 -2x^2 - 3x (a) Factor p completely. (b) Find the real zeros of p.... (answered by josgarithmetic)

Let p(x) = x^3 - 7x + 6 (a) Factor p completely [Hint: guess an initial zero and use... (answered by josgarithmetic)

Let p(x) = x^3 - 7x + 6 (a) Factor p completely [Hint: guess an initial zero and use... (answered by ankor@dixie-net.com)

P(X)=x^3-3x^2-5x+10 A) Evaluate P(x) for integers -3 through 5 B) Find all of the zeros (answered by MathLover1)

Let p(x) = x^6 - 3x^4 + 2x^2 Sketch the graph of p. (answered by josgarithmetic,Alan3354)

A polynomial P is given. P(x) = x^4 + 18x^2 + 81 (a) Factor P into linear and... (answered by MathLover1)

Let P(x)=x^3-2x^2-13x-10 a.determine whether x-5 is a factor if P(x). b.find another... (answered by ikleyn)

x^3-2x^2+10x a what are all the zeros of, real, and complex B: Factor P... (answered by josgarithmetic)