Page 631 - Algebra 1

LESSON Dividing Polynomials 93
Warm Up
1. Vocabulary A
(53)
monomials. Div_ide.
is a monomial or the sum or difference of
15x -3x _
72x2 - 8x (38) 8x
2
3.
2. Factor.
5x - 1 5. 25x2 -9
(83)
4. 2x2 +x-3 (75)
(43)
New Concepts A polynomial division problem can be written as a rational expression. To divide a polynomial by a monomial, divide each term in the numerator by the
denominator.
Dividing a Polynomial by a Monomial
Divide (8x3 + 12x2 + 4x) ÷ 4x. SOLUTION
Write as a rational expression.
Divide each term by the denominator.
Divide out common factors.
Example
1
(8x3 + 12x2 + 4x) ÷ 4x = (8x3 + 12x2 + 4x)
__ 4x
= 8x + 12x + 4x _3 _2 _
4x 4x 4x
2 8x3 2 312x2 1 4x
___
= 4x + 4x + 4x 11
= 2x2 + 3x + 1
Division of a polynomial by a binomial is similar to division of whole numbers.
Simplify.
Words
Numbers
32 · 4 _
4
Polynomials
Step 1
Factor the numerator and denominator, if possible.
128 = 32 · 4 __
44
x2 +4x+3 = (x+3)(x+1) ____
x+1 x+1
(x + 3)(x + 1) __
x+1
Step 2
Divide out any common factors.
Step 3
Simplify.
32
x+3
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