The problem is to find all the roots of the polynomial algebraically. To do this, I will use the factor theorem to factor the polynomial into linear factors. Then, I will set each factor equal to zero and solve for the roots.
Solution:
Factor the polynomial:
x^3 - 2x^2 - 35x = (x - 5)(x^2 + 5x + 7) = 0
Set each factor equal to zero and solve for the roots:
x - 5 = 0
x = 5
x^2 + 5x + 7 = 0
(x + 7)(x + 1) = 0
x = -7
x = -1
The roots of the polynomial are x = 5, -7, and -1.
Setup and find all roots of the polynomial algebraically (Not Graphing) :
x cubed minus two x squared minus thirty-five x equals zero
Understand & Think: Do you understand what is being asked and what you need to do? Do you have a list of things you know, ideas to try, and a plan for doing it? Identify the problem and list your strategies.
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