Question 1042746
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