Question

How to do synthetic division

Answer 1

Synthetic division is a method used to divide a polynomial by a binomial of the form (x - c). It involves arranging the polynomial in descending order, writing down the coefficients, and performing a series of multiplications and additions to obtain the quotient and remainder. Follow the step-by-step instructions to perform synthetic division.

Step-by-step explanation:

Synthetic division is a method used to divide a polynomial by a binomial of the form (x - c). Here are the steps:

1. Arrange the polynomial in descending order.
2. Write down the coefficients of the polynomial.
3. Put the divisor in the form (x - c).
4. Bring down the first coefficient.
5. Multiply the divisor by the coefficient and write the result under the next coefficient.
6. Add the column of numbers.
7. Repeat steps 5 and 6 until all coefficients have been used.
8. The final result is the quotient and the last number in the column is the remainder.

For example, let's divide the polynomial 2x^3 - 5x^2 + 3x + 1 by the binomial (x - 2).

Step 1: Arrange the polynomial in descending order: 2x^3 - 5x^2 + 3x + 1

Step 2: Write down the coefficients: 2, -5, 3, 1

Step 3: Put the divisor in the form (x - c): (x - 2)

Step 4: Bring down the first coefficient: 2

Step 5: Multiply the divisor by the coefficient and write the result under the next coefficient: (x - 2) * 2 = 2x - 4

Step 6: Add the column of numbers: -5 + 2x - 4 = 2x - 9

Step 7: Repeat steps 5 and 6: (x - 2) * (2x - 9) = 2x^2 - 13x + 18

Step 8: Repeat steps 5 and 6: (x - 2) * (2x^2 - 13x + 18) = 4x - 5

The quotient is 2x^2 - 13x + 18 and the remainder is 4x - 5.