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5.6 Dividing Polynomials

Dividing Polynomials To Divide a Polynomial by a Monomial Divide each term of the polynomial separately by the monomial.

Example Divide:

Dividing Polynomials To divide a polynomial by a polynomial other than a monomial, we use a process known as long division. Polynomial long division is similar to number long division, which we review on the next slide.

Dividing Polynomials Divide 43 into 72. Multiply 1 times 43. Subtract 43 from 72. Bring down 5. Divide 43 into 295. Multiply 6 times 43. Subtract 258 from 295. Bring down 6. Divide 43 into 376. Multiply 8 times 43. We then write our result as Subtract 344 from 376. Nothing to bring down.

Dividing Polynomials As you can see from the previous example, there is a pattern in the long division technique. Divide Multiply Subtract Bring down Then repeat these steps until you can’t bring down or divide any longer. We will incorporate this same repeated technique with dividing polynomials.

Dividing Polynomials 15 - 35 - x So our answer is 4x – 5. Divide 7x into 28x2. Multiply 4x times 7x+3. Subtract 28x2 + 12x from 28x2 – 23x. Bring down – 15. 15 - Divide 7x into –35x. 35 - x Multiply – 5 times 7x+3. Subtract –35x–15 from –35x–15. Nothing to bring down. So our answer is 4x – 5.

Dividing Polynomials Notice that the division process is continued until the degree of the remainder polynomial is less than the degree of the divisor polynomial.

Dividing Polynomials . 10 - 8 6 4 7 2 + - x x 14 4 + 8 + 20 - x 70 20 Divide 2x into 4x2. 8 6 4 7 2 + - x Multiply 2x times 2x+7. Subtract 4x2 + 14x from 4x2 – 6x. x 14 4 2 + 8 + Bring down 8. 20 - x Divide 2x into –20x. 70 20 - x Multiply -10 times 2x+7. Subtract –20x–70 from –20x+8. 78 Nothing to bring down. + ) 7 2 ( 78 x 10 - We write our final answer as .