Question

The polynomial p(x) = x3 – 7x - 6 has a known factor of (x + 1).

Rewrite p(x) as a product of linear factors.
p(x)

Answer 1

Hi there!

`\large\boxed{(x -3)(x + 2)(x + 1)}`

We can use long division to find the other roots of p(x).

We know that x + 1 is a factor, so:

Set up:

Find how many times that the first term in the divisor goes into the first of the dividend. Subtract from like terms.

x² - x - 6

x + 1 | x³ + 0x² - 7x - 6

x³ + x²

0 - x² - 7x

- x² - x

0 - 6x - 6

-6x - 6

0 0

Therefore, x² - x - 6 is another factor. We can factor this further:

Find two numbers that add up to -1 and multiply into -6. We get:

-3, 2

(x - 3)(x + 2)

The entire polynomial factored is:

(x -3)(x + 2)(x + 1)