Questions: Divide the following. Give your answer in the form quotient + (remainder / divisor) (-3x^2 - 17x + 13) / (3x - 1) =

Transcript text: Divide the following. Give your answer in the form quotient $+\frac{\text { remainder }}{\text { divisor }}$ \[ \frac{-3 x^{2}-17 x+13}{3 x-1}= \] $\square$ Question Help: Video Message instructor Calculator

Solution

Solution Steps

To solve the division of polynomials, we can use polynomial long division. The goal is to divide the polynomial $-3x^2 - 17x + 13$ by $3x - 1$ and express the result in the form of quotient plus remainder over divisor.

Step 1: Set Up the Division

We are given the polynomial division problem: \[ \frac{-3x^2 - 17x + 13}{3x - 1} \]

Step 2: Perform Polynomial Long Division

We divide $-3x^2 - 17x + 13$ by $3x - 1$. The quotient is $-x - 6$ and the remainder is $7$.

Step 3: Express the Result

The result of the division can be expressed in the form: \[ \text{quotient} + \frac{\text{remainder}}{\text{divisor}} \] Substituting the quotient and remainder, we get: \[ -x - 6 + \frac{7}{3x - 1} \]

Final Answer

\[ \boxed{-x - 6 + \frac{7}{3x - 1}} \]

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