Question

The polynomial p(x)=7^3-7x-6 has a known factor of (x+1) rewrite p(x) as a product of linear functions

Answer 1

Answer:

$p(x)=(x+1)(x+2)(x-3)$.

Step-by-step explanation:

Note: The given function is not correct.

Consider the given polynomial is

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

It is given that (x+1) is a factor of given function.

Using synthetic division, divide P(x) by (x+1) as shown below.

-1  |     1      0     -7      -6

    |           -1       1       6

--------------------------------------

        1       -1      -6       0

--------------------------------------

Bottom line represents the coefficients of quotient except the last element because it is remainder. So, the given function can be written as

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

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

$p(x)=(x+1)(x(x-3)+2(x-3))$

$p(x)=(x+1)(x+2)(x-3)$

Therefore, the function as a product of linear functions is $p(x)=(x+1)(x+2)(x-3)$.