Select all the functions that have a factor of x + 1.
r(x) = x^3 + 5x^2 + 7x + 3
g(x) = x^3 - 2x^2 - 7x - 4
h(x) = x^3 - 5x^2 + 2x + 8

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Select all the functions that have a factor of x + 1. r(x) = x^3 + 5x^2 + 7x + 3 g(x) = x^3 - 2x^2 - 7x - 4 h(x) = x^3 - 5x^2 + 2x + 8

SnapAndSolve AI · Accepted Answer

To determine if a function has a factor of x + 1, we can use the factor theorem, which states that if x + 1 is a factor of a polynomial, then substituting -1 into the polynomial should yield zero.

r(x) = x^3 + 5x^2 + 7x + 3
Substitute x = -1:
r(-1) = (-1)^3 + 5(-1)^2 + 7(-1) + 3 = -1 + 5 - 7 + 3 = 0
Therefore, r(x) has a factor of x + 1.
g(x) = x^3 - 2x^2 - 7x - 4
Substitute x = -1:
g(-1) = (-1)^3 - 2(-1)^2 - 7(-1) - 4 = -1 - 2 + 7 - 4 = 0
Therefore, g(x) has a factor of x + 1.
h(x) = x^3 - 5x^2 + 2x + 8
Substitute x = -1:
h(-1) = (-1)^3 - 5(-1)^2 + 2(-1) + 8 = -1 - 5 - 2 + 8 = 0
Therefore, h(x) has a factor of x + 1.

All functions r(x), g(x), and h(x) have a factor of x + 1.

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Select all the functions that have a factor of x + 1. r(x) = x^3 + 5x^2 + 7x + 3 g(x) = x^3 - 2x^2 - 7x - 4...

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