Question

The polynomial p ( x ) = x 3 − 7 x − 6 p(x)=x 3 −7x−6p, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 7, x, minus, 6 has a known factor of ( x + 1 ) (x+1)left parenthesis, x, plus, 1, right parenthesis. Rewrite p ( x ) p(x)p, left parenthesis, x, right parenthesis as a product of linear factors. p ( x ) = p(x)=p, left parenthesis, x, right parenthesis, equals

Answer 1

Answer:

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

Step-by-step explanation:

Answer 2

Answer:

$p(x)=x^3-7x-6 = (x+1)(x+2)(x-3)$

Step-by-step explanation:

Given that polynomial:

$p(x)=x^3-7x-6$

Known factor: $(x+1)$

To find:

Equation of the polynomial as the product of linear factors.

Solution:

The degree of polynomial is 3, and when we divide it by a linear equation, the result will be a quadratic.  That quadratic will have 2 solutions.

We can solve the quadratic in two linear factors and as a result we will have the answer.

First of all, we need to divide the polynomial $p(x)$ with the given factor $(x+1)$ to find the other factors.

$\dfrac{x^3-7x-6}{x+1} = x^2-x-6$

Solving the quadratic:

$x^2-x-6 = x^2-3x+2x-6\\\Rightarrow x(x-3)+2(x-3)\\\Rightarrow (x+2)(x-3)$

So, the answer is:

$p(x)=x^3-7x-6 = (x+1)(x+2)(x-3)$