Factoring Polynomials

Question

why is (x-3) NOT a factor of x^3+2x^2-5x-6?

Answer 1

It is not a factor since dividing x³ + 2x² - 5x - 6 by x - 3 results in a remainder of 24.

Answer 2

x^2 + 5x - 10

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(x - 3) _| x^3 + 2x^2 - 5x - 6

- x^3 - 3x^2 <if you cancel the left one, without correctly subtracting the right

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5x^2 - 5x <you might make it look like it works, but its wrong

- 5x^2 - 15x

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10x - 6

- -10x - 30

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24