Consider the polynomial function p(x) = x {}^(3) - 9x {}^(2) + 8x + 60 Divide P(x) by x - 6. Rewrite P(x) in a completely factored form. Please help! My teacher is really bad at…

Question

Consider the polynomial function


`p(x) = x {}^(3) - 9x {}^(2) + 8x + 60`
Divide P(x) by x - 6. Rewrite P(x) in a completely factored form.

Please help! My teacher is really bad at explaining things, we never went over how to do this, and I don't even get a text book to help me understand.
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Answer 1

The answer to your question is (x- 6)(x - 5)(x + 2)

Explanation:

Polynomial x³ - 9x² + 8x + 60

Divide by x - 6

x² - 3x - 10

x - 6 x³ - 9x² + 8x + 60

- x³ + 6x²

0 -3x² + 8x

+3x² - 18x

0 - 10x + 60

+10x -60

0 0 Remainder

Result (x² - 3x - 10)(x - 6)

Factor x² -3x - 10 = (x - 5)(x + 2)

Final result = (x- 6)(x - 5)(x + 2)