1. 4.7 Dividing Polynomials

2. Divide a polynomial by a monomial.
Objective 1
Divide a polynomial by a monomial.
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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
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4. Dividing a Polynomial by a Monomial
CLASSROOM EXAMPLE 1
Dividing a Polynomial by a Monomial
Divide 12m6 + 18m5 + 30m4 by 6m2.
Solution:
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5. Dividing a Polynomial by a Monomial
CLASSROOM EXAMPLE 2
Dividing a Polynomial by a Monomial
Divide
Solution:
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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:
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7. Dividing a Polynomial by a Monomial
CLASSROOM EXAMPLE 4
Dividing a Polynomial by a Monomial
Divide
Solution:
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8. Divide a polynomial by a polynomial.
Objective 2
Divide a polynomial by a polynomial.
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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.
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10. Divide a polynomial by a polynomial.
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11. Dividing a Polynomial by a Polynomial
CLASSROOM EXAMPLE 5
Dividing a Polynomial by a Polynomial
Divide
Solution:
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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.
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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:
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14. Dividing by a Polynomial with Missing Terms
CLASSROOM EXAMPLE 8
Dividing by a Polynomial with Missing Terms
Divide
Solution:
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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:
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