The polynomial p(x)=x^(3)+7x^(2)-36 has a known factor of (x+3). Rewrite p(x) as a product of linear factors. p(x)=

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The polynomial  p(x)=x^(3)+7x^(2)-36 has a known factor of  (x+3). Rewrite  p(x) as a product of linear factors.  p(x)=

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Factor Finding: Since we know that (x + 3) is a factor of p(x), we can perform polynomial long division or synthetic division to divide p(x) by (x + 3) to find the other factors.Synthetic Division Setup: Let's use synthetic division to divide p(x) by (x + 3). We set up the synthetic division with -3 (the zero of the factor x + 3) and the coefficients of p(x): 1 (for x^3), 7 (for x^2), 0 (for x, since there is no x term), and -36 (constant term).Performing Synthetic Division: Performing synthetic division, we bring down the leading coefficient (1) and then multiply it by -3 to get -3, which we add to the next coefficient (7) to get 4. We then multiply 4 by -3 to get -12, which we add to the next coefficient (0) to get -12. Finally, we multiply -12 by -3 to get 36, which we add to the last coefficient (-36) to get 0, confirming that (x + 3) is indeed a factor.Confirmation of Factor: The result of the synthetic division gives us the quotient polynomial q(x) = x^2 + 4x - 12. Now we need to factor q(x) to find the remaining linear factors of p(x).Factoring the Quotient Polynomial: We look for two numbers that multiply to -12 and add to 4. These numbers are 6 and -2. Therefore, we can factor q(x) as (x + 6)(x - 2).Writing the Polynomial as a Product: Now we can write p(x) as a product of its linear factors: p(x) = (x + 3)(x + 6)(x - 2).

The polynomial $p(x)=x^{3}+7 x^{2}-36$ has a known factor of $(x+3)$ . $\newline$ Rewrite $p(x)$ as a product of linear factors. $\newline$ $p(x)=$

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The polynomial p(x)=x3+7x2−36 p(x)=x^{3}+7 x^{2}-36 p(x)=x3+7x2−36 has a known factor of (x+3) (x+3) (x+3).\newlineRewrite p(x) p(x) p(x) as a product of linear factors.\newlinep(x)= p(x)= p(x)=

The polynomial $p(x)=x^{3}+7 x^{2}-36$ has a known factor of $(x+3)$ . $\newline$ Rewrite $p(x)$ as a product of linear factors. $\newline$ $p(x)=$