Question

Find the quotient and remainder when x^3 + 3x^2 – x – 7 is divided by x – 2

Answer 1

Let f(x) = x³ + 3x² - x - 7 is divided by x - 2.

Remember basic arithmetic: Dividend = Divisor x Quotient + Remainder.

Use Synthetic Division to divide polynomials:

    2| 1   3    -1     -7

      | 0   2   10    18

      |___________________

       1    5    9     | 11

Here Quotient is x² + 5x + 9 and Remainder is 11.

 

Or you can use long method of dividing:

x - 2)x³ + 3x² - x - 7(x² + 5x + 9

       x³ - 2x²

              5x² - x

              5x² - 10x

                    9x - 7

                    9x - 18

                           11

Therefore Quotient is x² + 5x + 9 and Remainder is 11.