Question

Divide and write the corresponding division statement.

{eq}frac {(2x^3 – 7x^2 + 16x – 22) }{ (2x-3)}

{/eq}

EXPERT ANSWER

We have to find the long division of $$displaystyle A= frac{2x^3-7x^2+16x-22}{2x-3}

$$

Apply the long division.

Step 1. Divide the leading coefficients of the numerator {eq}2x^3-7x^2+16x-22

{/eq} and the divisor {eq}2x-3.

{/eq}

Then we get Quotient {eq}=x^2

{/eq} and Remainder {eq}=-4x^2+16x-22.

{/eq}

Therefore, {eq}x^2+frac{-4x^2+16x-22}{2x-3}.

{/eq}

Step 2. Divide the leading coefficients of the numerator {eq}-4x^2+16x-22

{/eq} and the divisor {eq}2x-3.

{/eq}

Then we get Quotient {eq}=-2x

{/eq} and Remainder