Question

divide the following. give your answer in the form \\(\text{quotient}+\frac{\text{remainder}}{\text{divisor}}\\)\\(\frac{-6x^3 + 13x^2 - 20x + 25}{3x - 5}=\\)question help: video message instructorsubmit question jump to answer

Explanation:

Step1: Divide the leading terms

Divide the leading term of the dividend \(-6x^3\) by the leading term of the divisor \(3x\). We get \(\frac{-6x^3}{3x} = -2x^2\).

Step2: Multiply and subtract

Multiply the divisor \(3x - 5\) by \(-2x^2\): \(-2x^2(3x - 5) = -6x^3 + 10x^2\).
Subtract this from the dividend: \((-6x^3 + 13x^2 - 20x + 25) - (-6x^3 + 10x^2) = 3x^2 - 20x + 25\).

Step3: Divide the new leading terms

Divide the leading term of the new dividend \(3x^2\) by the leading term of the divisor \(3x\). We get \(\frac{3x^2}{3x} = x\).

Step4: Multiply and subtract

Multiply the divisor \(3x - 5\) by \(x\): \(x(3x - 5) = 3x^2 - 5x\).
Subtract this from the new dividend: \((3x^2 - 20x + 25) - (3x^2 - 5x) = -15x + 25\).

Step5: Divide the new leading terms

Divide the leading term of the new dividend \(-15x\) by the leading term of the divisor \(3x\). We get \(\frac{-15x}{3x} = -5\).

Step6: Multiply and subtract

Multiply the divisor \(3x - 5\) by \(-5\): \(-5(3x - 5) = -15x + 25\).
Subtract this from the new dividend: \((-15x + 25) - (-15x + 25) = 0\).

Step7: Combine the results

The quotient is \(-2x^2 + x - 5\) and the remainder is \(0\). So the division is \(-2x^2 + x - 5 + \frac{0}{3x - 5}\).

Answer:

\(-2x^2 + x - 5\)