SOLUTION: Let p(x) = x^3 - 7x + 6 (a) Factor p completely [Hint: guess an initial zero and use synthetic division]. (b) Find the real zeros of p. (c) Sketch the graph of p using a sign

Question 1156368: Let p(x) = x^3 - 7x + 6
(a) Factor p completely [Hint: guess an initial zero and use synthetic division].
(b) Find the real zeros of p.
(c) Sketch the graph of p using a sign diagram
Answer by josgarithmetic(39613) (Show Source): You can put this solution on YOUR website!
------

-3, 1, 2 are the real, rational roots.
You would pick from among -3, -1, -6, -2, 1, 2, 3, 6 to test using synthetic division.
ACCORDING TO USING RATIONAL ROOTS THEOREM, YOU PICK FROM -3, -1, -6, -2, 1, 2, 3, 6 , AND CHECK USING SYNTHETIC DIVISION.

(c):
Check any value within each of the intervals for the signs:
;
PICK ANY VALUE IN EACH INTERVAL AND DETERMINE THE SIGN OF p(x). YOU DO THIS.

(the graph)

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

1. Use synthetic division to divide p(x) = x^4 - 10x^2 - 2x + 4 by x + 3 2. Let f(x) = (answered by josgarithmetic)

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

Could someone please help? Use synthetic division and the Remainder Theorem to find... (answered by stanbon)

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)=x4 −2x3 −10x2 +6x+45 ▪ Use the Rational Zero Theorem to list all the... (answered by ikleyn)

Problem: Find all the real zeros of the polynomial. Use the quadratic formula if... (answered by rmromero)

Use synthetic division to show that the given x value is a zero of the polynomial. Then... (answered by josgarithmetic)