6.3 Dividing Polynomials

2

3232

3

12159

xy

xyxyyx 1.

When dividing by a monomial:Divide each term by the denominator

separately

2.ab

baabba

5

10155 4332

Dividing by a polynomial

• Long Division: rewrite it as a long division problem

51522 xxx

1525 2 xxx

1. 2.4642 23 xxxx

Dividing by a polynomial

• Synthetic Division– Step 1: Write the terms of the dividend so that the degrees

of the terms are in descending order. Then write just the coefficients.

– Step 2: Write the constant r of the divisor x – r to the left. Bring the first coefficient down.

– Step 3: Multiply the first coefficient by r . Write the product under the second coefficient. Then add the product and the second coefficient.

– Step 4: Multiply the sum by r. Write the product under the next coefficient and add. Repeat until finished.

– Step 5: rewrite the coefficient answers with appropriate x values

ex 1: Use synthetic division to find (x3 – 4x2 + 6x – 4) ÷ (x – 2).

• Step 1 • Steps 2-4

• Step 5

x3 – 4x2 + 6x – 4 1 - 4 6 - 4

1 - 4 6 - 4

1

2

- 2

- 4

2

4

0

x2 – 2x + 2

Use synthetic division to solve each problem

2

81213 23

x

xxx 124 12448 xxxx2. 3.