Question

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

Answer 1

Answer:

Using synthetic division suffices to answer your question:

Step-by-step explanation:

Synthetic division is the process by one reduces a large polynomial in your case $x^3-7x-6$ by a binomial in your case $(x+1)$.

To do so one does the following:

$\begin{array}{cccccc}-1|& 1&0&-7&-6\\ & &-1&1&6 \\& 1&-1&-6&0 \end{array}$

Since we divided by a linear binomial it reduces the power by one which produces the following quadratic:

$(x^2-x-6)$

Which can be factored in the following, and I will provide the complete factorization as well:

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