Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Chapter 4 Polynomials

1-2 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Division of Polynomials Dividing by a Monomial Dividing by a Binomial 4.8

1-3 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Dividing by a Monomial To divide a polynomial by a monomial, we divide each term by the monomial.

1-4 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Divide. x x 4  12x 3 by 6x Solution

1-5 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Divide: Solution

1-6 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Dividing by a Binomial For divisors with more than one term, we use long division, much as we do in arithmetic. Polynomials are written in descending order and any missing terms in the dividend are written in, using 0 for the coefficients.

1-7 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Divide x 2 + 7x + 12 by x + 3. Solution Now we “bring down” the next term. Subtract by changing signs and adding Multiply x + 3 by x, using the distributive law

1-8 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Subtract Multiply 4 by the divisor, x + 3, using the distributive law

1-9 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example Divide 15x 2  22x + 14 by 3x  2. Solution The answer is 5x  4 with R6. Another way to write the answer is

1-10 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Example The answer is Divide x 5  3x 4  4x x by x  3. Solution