SOLUTION: for f(x)= x^3-7x^2+8x+16, a, find f(10) using synthetic division. b, is 10 a zero of the function? Explain. c, use synthetic division to determine if x+1 is a factor of f(x). d

Question 961904: for f(x)= x^3-7x^2+8x+16,
a, find f(10) using synthetic division.
b, is 10 a zero of the function? Explain.
c, use synthetic division to determine if x+1 is a factor of f(x).
d, is -1 a zero of the function? Explain.
e, list all of the zeros of the polynomial.
f, write the polynomial function as a product of linear factors
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Review the Factor and the Remainder Theorems.

If the synthetic division for checking a possible root gives a remainder, this means that the root checked is (*) not a root of the function, and (*) the remainder is the value of the function at that x value which has given that remainder r, or checking any root c, . THAT will guide you in answering some of your questions. In case the remainder were 0, this means that the value c checked is a root.

If you know how to do synthetic division, then the possible roots to check are -1, -2, -4, -8, -16, 1, 2, 4, 8, 16. Not more than any three of them would be found to be roots of f.
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