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.
​

Answer 1

Answer:

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

Step-by-step 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)