The polynomial p(x)=x^3-7x-6 has a known factor of (x+1). rewrite p(x) as a product of linear factors Posted on October 22, 2021 By Gafran 4 Comments on The polynomial p(x)=x^3-7x-6 has a known factor of (x+1). rewrite p(x) as a product of linear factors the polynomial p(x)=x^3-7x-6 has a known factor of (x+1). rewrite p(x) as a product of linear factors Mathematics
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 factorsReply
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]Reply
(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)