The polynomial p(x)=3x^(3)-5x^(2)-4x+4 has a known factor of (x-2). Rewrite p(x) as a product of linear factors. p(x)=

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The polynomial  p(x)=3x^(3)-5x^(2)-4x+4 has a known factor of  (x-2). Rewrite  p(x) as a product of linear factors.  p(x)=

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Perform polynomial long division or synthetic division: Since we know that (x-2) is a factor of p(x), we can perform polynomial long division or synthetic division to divide p(x) by (x-2).Set up synthetic division with known factor: Set up the synthetic division with the root of the known factor, which is 2, and the coefficients of p(x): 3, -5, -4, and 4.Perform synthetic division: Perform the synthetic division. Bring down the leading coefficient (3) to the bottom row.Multiply root by value and write result: Multiply the root (2) by the value just brought down (3) and write the result (6) under the next coefficient (-5).Add values and write result: Add the values in the second column (-5 + 6 = 1) and write the result (1) in the bottom row.Repeat the process: Repeat the process: multiply the root (2) by the new value in the bottom row (1) to get 2, and write this under the next coefficient (-4).Add values and write result: Add the values in the third column (-4 + 2 = -2) and write the result (-2) in the bottom row.Repeat the process one last time: Repeat the process one last time: multiply the root (2) by the new value in the bottom row (-2) to get -4, and write this under the last coefficient (4).Confirm (x-2) as a factor: Add the values in the last column (4 + (-4) = 0) and write the result (0) in the bottom row. Since the remainder is 0, this confirms that (x-2) is indeed a factor of p(x).Coefficients of quotient polynomial: The result of the synthetic division gives us the coefficients of the quotient polynomial, which are 3, 1, and -2. This means p(x) can be written as (x-2)(3x^2 + x - 2).Factor the quadratic polynomial: Now we need to factor the quadratic polynomial 3x^2 + x - 2. We look for two numbers that multiply to -6 (3 * -2) and add to 1 (the coefficient of x). These numbers are 2 and -3.Write quadratic polynomial as a product: Write the quadratic polynomial as a product of two binomials using the numbers found in the previous step: 3x^2 + x - 2 = (3x - 2)(x + 1).Combine factors to express p(x): Combine the factors to express p(x) as a product of linear factors: p(x) = (x - 2)(3x - 2)(x + 1).

The polynomial $p(x)=3 x^{3}-5 x^{2}-4 x+4$ has a known factor of $(x-2)$ . $\newline$ Rewrite $p(x)$ as a product of linear factors. $\newline$ $p(x)=$

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The polynomial p(x)=3x3−5x2−4x+4 p(x)=3 x^{3}-5 x^{2}-4 x+4 p(x)=3x3−5x2−4x+4 has a known factor of (x−2) (x-2) (x−2).\newlineRewrite p(x) p(x) p(x) as a product of linear factors.\newlinep(x)= p(x)= p(x)=

The polynomial $p(x)=3 x^{3}-5 x^{2}-4 x+4$ has a known factor of $(x-2)$ . $\newline$ Rewrite $p(x)$ as a product of linear factors. $\newline$ $p(x)=$