4.7 Dividing Polynomials

Divide a polynomial by a monomial. Objective 1 Divide a polynomial by a monomial. Slide 4.7-3

Dividing a polynomial by a monomial. We add two fractions with a common denominator as follows. In reverse this statement gives a rule for dividing a polynomial by a monomial: Dividing A Polynomial by a Monomial To divide a polynomial by a monomial, divide each term of the polynomial by the monomial: Examples: and Divisor Dividend Quotient Slide 4.7-4

Dividing a Polynomial by a Monomial CLASSROOM EXAMPLE 1 Dividing a Polynomial by a Monomial Divide 12m6 + 18m5 + 30m4 by 6m2. Solution: Slide 4.7-5

Dividing a Polynomial by a Monomial CLASSROOM EXAMPLE 2 Dividing a Polynomial by a Monomial Divide Solution: Slide 4.7-6

CLASSROOM EXAMPLE 3 Divide −8p4 − 6p3 − 12p5 by −3p3. Solution: Dividing a Polynomial by a Monomial with a Negative Coefficient Divide −8p4 − 6p3 − 12p5 by −3p3. Solution: Slide 4.7-7

Dividing a Polynomial by a Monomial CLASSROOM EXAMPLE 4 Dividing a Polynomial by a Monomial Divide Solution: Slide 4.7-8

Divide a polynomial by a polynomial. Objective 2 Divide a polynomial by a polynomial. Slide 4.7-9

Divide a polynomial by a polynomial. To divide a polynomial by a polynomial (other than a monomial). Both polynomials must first be written in descending powers. Slide 4.7-10

Divide a polynomial by a polynomial. Slide 4.7-11

Dividing a Polynomial by a Polynomial CLASSROOM EXAMPLE 5 Dividing a Polynomial by a Polynomial Divide Solution: Slide 4.7-12

Dividing a Polynomial by a Polynomial CLASSROOM EXAMPLE 6 Dividing a Polynomial by a Polynomial Divide Solution: Remember to include “ ” as part of the answer. Slide 4.7-13

Dividing into a Polynomial with Missing Terms CLASSROOM EXAMPLE 7 Dividing into a Polynomial with Missing Terms Divide x3 − 8 by x − 2. Solution: Slide 4.7-14

Dividing by a Polynomial with Missing Terms CLASSROOM EXAMPLE 8 Dividing by a Polynomial with Missing Terms Divide Solution: Slide 4.7-15

CLASSROOM EXAMPLE 9 Divide 3x3 + 7x2 + 7x + 11 by 3x + 6. Solution: Dividing a Polynomial When the Quotient Has Fractional Coefficients Divide 3x3 + 7x2 + 7x + 11 by 3x + 6. Solution: Slide 4.7-16