The polynomial p(x)=5x^(3)-9x^(2)-6x+8 has a known factor of (x+1). Rewrite p(x) as a product of linear factors. p(x)=

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The polynomial  p(x)=5x^(3)-9x^(2)-6x+8 has a known factor of  (x+1). Rewrite  p(x) as a product of linear factors.  p(x)=

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Factor Finding: Since we know that (x + 1) is a factor of p(x), we can use polynomial long division or synthetic division to divide p(x) by (x + 1) to find the other factors.Synthetic Division: Let's perform synthetic division using the root of the known factor, which is x = -1. We set up the synthetic division as follows:  -1 |  5  -9  -6  8        ------------           5  -14  8  0  We bring down the 5, multiply it by -1 to get -5, and add it to -9 to get -14. We then multiply -14 by -1 to get 14, and add it to -6 to get 8. Finally, we multiply 8 by -1 to get -8, and add it to 8 to get 0, which confirms that (x + 1) is a factor since the remainder is 0.Quotient Polynomial: The result of the synthetic division gives us the coefficients of the quotient polynomial, which is 5x^2 - 14x + 8. So, p(x) can be written as (x + 1)(5x^2 - 14x + 8).Factoring Quadratic Polynomial: Now we need to factor the quadratic polynomial 5x^2 - 14x + 8. We can try to factor it by looking for two numbers that multiply to 5*8 = 40 and add up to -14.Grouping and Factoring: The two numbers that satisfy these conditions are -10 and -4, since (-10) * (-4) = 40 and (-10) + (-4) = -14. So we can write the quadratic as 5x^2 - 10x - 4x + 8.Common Factor Extraction: Now we can factor by grouping. We group the terms as follows: (5x^2 - 10x) + (-4x + 8).Complete Factoring: We factor out the common factors from each group: 5x(x - 2) - 4(x - 2).Final Result: Since both terms have a common factor of (x - 2), we can factor it out to get (5x - 4)(x - 2).Now we have factored p(x) completely into linear factors: p(x) = (x + 1)(5x - 4)(x - 2).

The polynomial $p(x)=5 x^{3}-9 x^{2}-6 x+8$ has a known factor of $(x+1)$ . $\newline$ Rewrite $p(x)$ as a product of linear factors. $\newline$ $p(x)=$

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The polynomial p(x)=5x3−9x2−6x+8 p(x)=5 x^{3}-9 x^{2}-6 x+8 p(x)=5x3−9x2−6x+8 has a known factor of (x+1) (x+1) (x+1).\newlineRewrite p(x) p(x) p(x) as a product of linear factors.\newlinep(x)= p(x)= p(x)=

The polynomial $p(x)=5 x^{3}-9 x^{2}-6 x+8$ has a known factor of $(x+1)$ . $\newline$ Rewrite $p(x)$ as a product of linear factors. $\newline$ $p(x)=$