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$p(x)=3x^3-20x^2+37x-20$ has a known factor of $(x-4)$ Rewrite $p(x)$ as a product of linear factors.

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Factor polynomials

Full solution

Q.

p(x)=3x^3-20x^2+37x-20

has a known factor of

(x-4)

Rewrite

p(x)

as a product of linear factors.

Perform Polynomial Division: Step Title: Perform Polynomial Division $\newline$ Calculation: Divide $p(x)$ by $(x-4)$ using synthetic division or long division.
Set Up Synthetic Division: Step Title: Set Up Synthetic Division $\newline$ Calculation: Set up synthetic division with $4$ as the zero and the coefficients of $p(x)$ as $3$ , $-20$ , $37$ , $-20$ .
Carry Out Synthetic Division: Step Title: Carry Out Synthetic Division $\newline$ Calculation: Bring down the $3$ , multiply by $4$ to get $12$ , add to $-20$ to get $-8$ , multiply by $4$ to get $-32$ , add to $37$ to get $5$ , multiply by $4$ to get $4$ $0$ , add to $-20$ to get $4$ $2$ .
Write Down the Resulting Polynomial: Step Title: Write Down the Resulting Polynomial $\newline$ Calculation: The resulting polynomial from the synthetic division is $3x^2 - 8x + 5$ .
Factor the Quadratic Polynomial: Step Title: Factor the Quadratic Polynomial $\newline$ Calculation: Look for two numbers that multiply to $3\times5=15$ and add up to $-8$ . The numbers are $-3$ and $-5$ .
Write the Factored Form: Step Title: Write the Factored Form of the Quadratic $\newline$ Calculation: The factored form of the quadratic is $(3x - 5)(x - 3)$ .
Combine All Factors: Step Title: Combine All Factors $\newline$ Calculation: Combine the known factor $(x - 4)$ with the factored form of the quadratic to get the final factored form of $p(x)$ .

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