Lesson 11-5

Example 1 Divide Polynomials by Monomials
a.  Find (8x + 2) 4x.
	(8x + 2) 4x = 	Write as a rational expression.
		=  + 	Divide each term by 4x.

		=  + 	Simplify each term.

		= 2x + 	Simplify.

b.  Find 14ab – 7ab + 21a  7ab.
	14ab – 7ab + 21a  7ab = 	Write as a rational expression.
		=  –  + 	Divide each term by 7ab.

		=  –  + 	Simplify each term.

		= 2a – 1 + 	Simplify.

Example 2 Divide a Polynomial by a Binomial
Find (2r - 5r +3)  (r – 1).
	(2r – 5r +3)  (r – 1) = 	Write as a rational expression.
		= 	Factor the numerator.

		= 	Divide by the GCF.

		= 2r – 3	Simplify.

Example 3 Long Division
Find (6x + 5x – 3) (3x + 1).
The expression 6x + 5x – 3 cannot be factored, so use long division.
Step 1	Divide the first term of the dividend, 6x, by the first term of the divisor, 3x.

	Step 2	Divide the first term of the partial dividend, 3x – 3, by the first term of the divisor, 3x.

The quotient of (6x + 5x – 3) (3x + 1) is 2x + 1 with a remainder of –4, which can be written as
2x + 1 - . Since there is a nonzero remainder, 3x + 1 is not a factor of 6x + 5x – 3.

Example 4 Polynomial with Missing Terms
Find (2x - x + 1) (x + 1).

Insert an x term that has a coefficient of 0.
		
Therefore, (2x - x + 1) (x + 1) = 2x- 3x + 3 - .