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2. 5.7 Dividing Polynomials Divide a polynomial by a monomial.
Divide a polynomial by a polynomial. 1 2
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3. Divide a polynomial by a monomial.
Objective 1
Divide a polynomial by a monomial.
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4. 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:
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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5. EXAMPLE 1 Divide 12m6 + 18m5 + 30m4 by 6m2. Solution:
Dividing a Polynomial by a Monomial
Divide 12m6 + 18m5 + 30m4 by 6m2.
Solution:
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6. EXAMPLE 2 Divide Solution: Dividing a Polynomial by a Monomial
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7. EXAMPLE 3 Divide −8p4 − 6p3 − 12p5 by −3p3. Solution:
Dividing a Polynomial by a Monomial with a Negative Coefficient
EXAMPLE 3
Divide −8p4 − 6p3 − 12p5 by −3p3.
Solution:
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8. EXAMPLE 4 Divide Solution: Dividing a Polynomial by a Monomial
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9. Divide a polynomial by a polynomial.
Objective 2
Divide a polynomial by a polynomial.
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10. 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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11. Divide a polynomial by a polynomial. (cont’d)
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12. EXAMPLE 5 Divide Solution: Dividing a Polynomial by a Polynomial
Remember to include “ ” as part of the answer.
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13. EXAMPLE 6 Divide x3 − 8 by x − 2. Solution:
Dividing into a Polynomial with Missing Terms
Divide x3 − 8 by x − 2.
Solution:
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14. EXAMPLE 7 Divide Solution: Dividing by a Polynomial with Missing Terms
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15. EXAMPLE 8 Divide 3x3 + 7x2 + 7x + 11 by 3x + 6. Solution:
Dividing a Polynomial when the Quotient Has Fractional Coefficients
EXAMPLE 8
Divide 3x3 + 7x2 + 7x + 11 by 3x + 6.
Solution:
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