6 3 Dividing Polynomials MAIN IDEAS DIVIDE POLYNOMIALS

6. 3 Dividing Polynomials MAIN IDEAS • DIVIDE POLYNOMIALS USING LONG DIVISION.

Division Polynomial ÷ Monomial Rewrite the division problem as individual monomial division problems and simplify. 1) 9 x²y³ – 15 xy² + 12 xy³ 3 xy² 3) (18 x²y + 27 x³y²z)(3 xy)⁻² 2) 16 a⁵b³ – 20 ab⁵ 4 ab⁷

Long Division Polynomial ÷ Polynomial • • Use long division. When dividing polynomials they must be written in descending order and every degree must be accounted for. 1) (x² + 7 x – 30) ÷ (x – 3)

Example 2) (x³ + 13 x² – 12 x – 8)(x + 2)⁻¹

Synthetic Division Polynomial ÷ Binomial Synthetic Division • • • An easier process for dividing a polynomial by a 1 st degree binomial. It uses the coefficients of the dividend and the constant of the divisor. Every coefficient, even the skipped variables, must be accounted.

Synthetic Division 1) Write the dividend in descending order. Then write just the coefficients. 2) Write the constant of the divisor to the left. 3) Bring down the lead coefficient. 4)Multiply the lead coefficient and divisor. Put this under the 2 nd coefficient and add. 5)Then write each # with the appropriate variable. (5 x ³– 13 x² + 10 x – 8) ÷ (x – 2)

Synthetic Division 1) (3 x³ – 8 x² + 11 x – 14) ÷ (x – 2)

Synthetic division 2) (x³ - 6) ÷ (x + 2)