The polynomial p(x)=x^(3)-6x^(2)+32 has a known factor of (x-4). Rewrite p(x) as a product of linear factors. p(x) = ◻

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Factor Out Known Factor: Factor out the known factor from the polynomial. Since we know that (x - 4) is a factor of p(x), we can perform polynomial division or use synthetic division to divide p(x) by (x - 4) to find the other factors.Perform Synthetic Division: Perform the synthetic division using the known factor (x - 4). We set up the synthetic division with the root of the known factor, which is 4, and the coefficients of p(x), which are 1, -6, and 32.     4 |  1  -6   0   32     |     4  -8  -32     -----------------       1  -2  -8   0  The result of the synthetic division gives us the coefficients of the quotient polynomial: 1x^2 - 2x - 8.Factor Quotient Polynomial: Factor the quotient polynomial. The quotient polynomial is a quadratic, which we can factor further if possible. We look for two numbers that multiply to -8 and add up to -2. These numbers are -4 and 2.Write Factored Form: Write the factored form of the quotient polynomial. The factored form of the quadratic is (x - 4)(x + 2). Therefore, we can write p(x) as the product of its factors: p(x) = (x - 4)(x - 4)(x + 2).Simplify Repeated Factor: Simplify the repeated factor. Since (x - 4) is a factor that appears twice, we can write it as a squared term: p(x) = (x - 4)^2(x + 2).

The polynomial $p(x)=x^{3}-6 x^{2}+32$ has a known factor of $(x-4)$ . $\newline$ Rewrite $p(x)$ as a product of linear factors. $\newline$ $p(x) = \square$

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The polynomial p(x)=x3−6x2+32 p(x)=x^{3}-6 x^{2}+32 p(x)=x3−6x2+32 has a known factor of (x−4) (x-4) (x−4).\newlineRewrite p(x) p(x) p(x) as a product of linear factors.\newlinep(x)=□ p(x) = \square p(x)=□

The polynomial $p(x)=x^{3}-6 x^{2}+32$ has a known factor of $(x-4)$ . $\newline$ Rewrite $p(x)$ as a product of linear factors. $\newline$ $p(x) = \square$