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

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

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

Because..

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

Step-by-step explanation:

x³ - 7x - 6

(x+1) (x² - x - 6) found by doing long division

(x+1) ( x - 3) (x + 2) are the factors

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 [tex]x^3-7x-6[/tex] by a binomial in your case [tex](x+1)[/tex].

To do so one does the following:

[tex]\begin{array}{cccccc}-1|& 1&0&-7&-6\\ & &-1&1&6 \\& 1&-1&-6&0 \end{array}[/tex]

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

[tex](x^2-x-6)[/tex]

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

[tex]p(x)=(x+1)(x-3)(x+2)[/tex]

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