Page 632 - Algebra 1

Example
2
Dividing a Polynomial by a Binomial
Divide each expression.
a. (x2 - 6x + 9) ÷ (x - 3) SOLUTION
(x2 - 6x + 9) ÷ (x - 3) = x2 -6x+9
__ x-3
Write as a rational expression. Factor the numerator.
Divide out common factors. Simplify.
Write as a rational expression.
Factor the numerator.
Write the denominator in descending order. Factor out a -1 in the denominator.
Divide out common factors.
Simplify.
= (x-3)(x-3) __
x-3
= (x-3)(x-3)
__ (x - 3)
=x-3
b. (x2 - 5x + 6) ÷ (2 - x) SOLUTION
(x2 - 5x + 6) ÷ (2 - x) = x2 -5x+6
__ 2-x
= (x-3)(x-2) __
Hint
When the signs of the binomials, one in the numerator and one in the denominator, are opposites, factor out -1.
2-x
= (x-3)(x-2)
__ -x + 2
= (x-3)(x-2) __
-1(x - 2) = (x-3)(x-2)
__ -1(x - 2)
= -x + 3
Just as with whole numbers, long division can also be used to divide polynomials.
27 x+2
21 567
-_4_2 147
-__14_7 00
x+1 x2 +3x+2
-(x2 +x) _____
2x + 2 -(2x + 2)
_____
Lesson 93 617