Question

What is the remainder for the division expression (16x^3 + 20x^2 - 4x - 5) divided by (2x - 3)

Answer 1

Remainder = 88

Explanation:

To divide (16x³ + 20x² - 4x - 5) by (2x - 3) we can use the long division method of dividing polynomials.

Long Division Method of dividing polynomials

1. Divide the first term of the dividend by the first term of the divisor and put that in the answer.
2. Multiply the divisor by that answer, put that below the dividend and subtract to create a new polynomial.
3. Repeat until no more division is possible.
4. Write the solution as the quotient plus the remainder divided by the divisor.

Given:

• Dividend: 16x³ + 20x² - 4x - 5
• Divisor: 2x - 3

Carry out the long division:

`\large \begin{array}{r}8x^2+22x+31\phantom{)}\\2x-3{\overline{\smash{\big)}\,16x^3 + 20x^2 - 4x - 5\phantom{)}}}\\{-~\phantom{(}\underline{(16x^3-24x^2)\phantom{-bbbbbb.)}}\\44x^2-4x-5\phantom{)}\\-~\phantom{()}\underline{(44x^2-66x)\phantom{b...}}\\62x-5\phantom{)}\\-~\phantom{()}\underline{(62x-93)}\\88\phantom{)}\end{array}`

Therefore:

• Quotient: 8x² + 22x + 31
• Remainder: 88

Write the solution as the quotient plus the remainder divided by the divisor. Therefore, the solution is:

`8x^2 + 22x + 31+(88)/(2x-3)`

`\hrulefill`

Definitions

• Dividend: The polynomial which has to be divided.
• Divisor: The expression by which the dividend is divided.
• Quotient: The result of the division.
• Remainder: The part left over.