SOLUTION: Use the Factor Theorem to determine whether x - c is a factor of f(x). 8x3 + 36x2 - 19x

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Question 1042746: Use the Factor Theorem to determine whether x - c is a factor of f(x).
8x3 + 36x2 - 19x - 5; x + 5
a. Yes
b. No

Found 2 solutions by jim_thompson5910, ikleyn:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
x+5 is really x - (-5)

x - (-5) is in the form x - c where c = -5 in this case.

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Remainder Theorem: if x - c is a factor of f(x), then f(c) = 0. This works both ways. If f(c) = 0, then x-c is a factor of f(x).

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Use the remainder theorem to see if plugging x = -5 into f(x) yields 0.

y = 8x^3 +36x^2 - 19x - 5
y = 8(-5)^3 +36(-5)^2 - 19(-5) - 5
y = 8(-125) +36(25) - 19(-5) - 5
y = -1000 + 900 + 95 - 5
y = -100 + 95 - 5
y = -5 - 5
y = -10

The result is -10 which is NOT zero. Since it's not zero, this means that x+5 is NOT a factor of f(x).

Note: if you change y = 8x^3 +36x^2 - 19x - 5 to y = 8x^3 +36x^2 - 19x + 5, then x+5 would be a factor

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
.
On the Remainder Theorem see the lesson
    - Divisibility of polynomial f(x) by binomial x-a
in this site.

SOLUTION: Use the Factor Theorem to determine whether x - c is a factor of f(x). 8x3 + 36x2 - 19x - 5; x + 5 a. Yes b. No