Question

If f(x) = 5x² + 2, then what is the
remainder when f(x) is divided by
x + 2?

Answer 1

Answer: I think it's 5.

Answer 2

22

Explanation:

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.

Long Division Method of dividing polynomials

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

Given:

• Dividend: 5x² + 2
• Divisor: x + 2

Using long division to find the remainder:

`\large \begin{array}{r}5x-10\phantom{)}\\x+2{\overline{\smash{\big)}\,5x^2\phantom{bbbbbbb)}+2\phantom{)}}}\\{-~\phantom{(}\underline{(5x^2+10x)\phantom{bbbb..}}\\-10x\phantom{)}+2\phantom{)}\\-~\phantom{()}\underline{(-10x-20)\phantom{}}\\22\phantom{)}\\\end{array}`

Solution:

`(5x^2+2)/(x+2)=5x-10+(22)/(x+2)`

Therefore:

• Quotient: 5x - 10
• Remainder: 22