Factor Theorem Test

Question 1 of 5: Determine if g(x) is a factor of f(x):

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$$f(x)=x^5 - 5x^4 + 5x^3 - 25x^2 - 6x + 30$$ $$g(x)=x - 5$$

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Yes

Question 2 of 5: Determine if g(x) is a factor of f(x):

$$f(x)=x^5 - 3x^4 - 8x^3 + 24x^2 - 9x + 27$$ $$g(x) =x + 1$$

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Yes

Question 3 of 5: Determine if g(x) is a factor of f(x):

$$f(x)=x^4 + 2x^3 - 27x - 54$$ $$g(x) =x + 2$$

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Yes

Question 4 of 5: f(k) = 0, factor f(x):

$$f(x)=x^3 + 7x^2 + 16x + 12$$ $$k=-2$$

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$$f(x) = (x + 2)(x - 2)(x + 3)$$

$$f(x) = (x + 2)^2 (x - 1)$$

$$f(x) = (x + 2)(x - 4)(x + 3)$$

$$f(x) = (x + 2)^2 (x + 3)$$

$$f(x) = (x + 2)(x^2 - 2)(x + 3)$$

Question 5 of 5: f(k) = 0, factor f(x):

$$f(x)=x^3 + 5x^2 - 4x - 20$$ $$k=2$$

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$$f(x) = (x + 1)(x - 2)(x - 1)$$

$$f(x) = (x + 5)(x + 2)^2$$

$$f(x) = (x + 5)(x + 2)(x - 2)$$

$$f(x) = x(x + 5)(x + 2)$$

$$f(x) = (x + 3)(x + 1)(x - 2)$$

Great Job! You Passed!

Better Luck Next Time...