Question

divide.
\\((4x^3 - 14x^2 + 20x - 9) \div (2x^2 - 2x)\\)
your answer should give the quotient and the remainder.
quotient:
remainder:

Explanation:

Step1: Divide leading terms

Divide the leading term of the dividend \(4x^3\) by the leading term of the divisor \(2x^2\). So, \(\frac{4x^3}{2x^2} = 2x\). This is the first term of the quotient.

Step2: Multiply divisor by \(2x\)

Multiply the divisor \(2x^2 - 2x\) by \(2x\): \(2x(2x^2 - 2x)=4x^3 - 4x^2\).

Step3: Subtract from dividend

Subtract this from the original dividend: \((4x^3 - 14x^2 + 20x - 9)-(4x^3 - 4x^2)= -10x^2 + 20x - 9\).

Step4: Divide new leading term

Divide the leading term of the new dividend \(-10x^2\) by the leading term of the divisor \(2x^2\): \(\frac{-10x^2}{2x^2}=-5\). This is the next term of the quotient.

Step5: Multiply divisor by \(-5\)

Multiply the divisor \(2x^2 - 2x\) by \(-5\): \(-5(2x^2 - 2x)=-10x^2 + 10x\).

Step6: Subtract to get remainder

Subtract this from the new dividend: \((-10x^2 + 20x - 9)-(-10x^2 + 10x)=10x - 9\).

Answer:

Quotient: \(2x - 5\)
Remainder: \(10x - 9\)