5 6 Dividing Polynomials Dividing Polynomials Dividing a

§ 5. 6 Dividing Polynomials

Dividing Polynomials Dividing a Polynomial by a Monomial Divide each term of the polynomial by the monomial. Example: Martin-Gay, Beginning and Intermediate Algebra, 4 ed 2

Dividing Polynomials Dividing a polynomial by a polynomial other than a monomial uses a “long division” technique that is similar to the process known as long division in dividing two numbers, which is reviewed on the next slide. Martin-Gay, Beginning and Intermediate Algebra, 4 ed 3

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. Subtract 344 from 376. Nothing to bring down. We then write our result as Martin-Gay, Beginning and Intermediate Algebra, 4 ed 4

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. Martin-Gay, Beginning and Intermediate Algebra, 4 ed 5

Dividing Polynomials Using Long Division Example: Divide: 1. Divide the leading term of the dividend, c 2, by the first term of the divisor, x. 2. Multiply c by c + 1. 3. Subtract c 2 + c from c 2 + 3 c – 2. Continued. Martin-Gay, Beginning and Intermediate Algebra, 4 ed 6

Dividing Polynomials Using Long Division Example continued: Bring down the next term to obtain a new polynomial. 4. Repeat the process until the degree of the remainder is less than the degree of the binomial divisor. 2 c Remainder 5. Check by verifying that (Quotient)(Divisor) + Remainder = Dividend. Martin-Gay, Beginning and Intermediate Algebra, 4 ed 7

Dividing Polynomials Divide 7 x into 28 x 2. Multiply 4 x times 7 x + 3. Subtract 28 x 2 + 12 x from 28 x 2 – 23 x. Bring down – 15. - 35 x - 15 Divide 7 x into – 35 x. Multiply – 5 times 7 x + 3. Subtract – 35 x – 15 from – 35 x – 15. Nothing to bring down. So our answer is 4 x – 5. Martin-Gay, Beginning and Intermediate Algebra, 4 ed 8

Dividing Polynomials 2 x - 10 2 2 x + 7 4 x - 6 x + 8 2 4 x + 14 x -20 x + 8 -20 x - 70 78 Divide 2 x into 4 x 2. Multiply 2 x times 2 x+7. Subtract 4 x 2 + 14 x from 4 x 2 – 6 x. Bring down 8. Divide 2 x into – 20 x. Multiply -10 times 2 x+7. Subtract – 20 x– 70 from – 20 x+8. Nothing to bring down. 78 We write our final answer as 2 x - 10 + ( 2 x + 7) Martin-Gay, Beginning and Intermediate Algebra, 4 ed 9