Page 254 - Algebra 1

Caution
To completely factor a polynomial, you must factor out the greatest common factor, not just a common factor.
b. 9x4y2 - 9x6y
SOLUTION
The GCF of the polynomial is 9x4y. 9x4y2 -9x6y=9x4y·y-9x4y·x2
The factored polynomial is 9x4y (y - x2).
Fractions can be simplified if the numerator and denominator contain common factors. This is because the operations of multiplication and division undo each other.
numeric fractions: _4 = _2 and _8 = _2 or 2 10 5 4 1
___ algebraic fractions: 4x = 2x and 8x = 2x
Notice that there is no addition or subtraction involved in the fractions above. Simplifying fractions with addition or subtraction in the numerator follows similar rules to adding or subtracting numeric fractions. A fraction can only be simplified if the numerator and the denominator have common factors.
Simplifying Algebraic Fractions
10 5 4
Example
4
Simplify each expression.
_3 p + 3 3 SOLUTION
_3 p + 3
_3
= 3(p + 1)
3 = p +_1
5x - 25x2 b. 5xy .
S_OLUTION 5x - 25x2
_5xy
= 5x(1 - 5x)
_ 5xy
= 1 - 5x y
a.
Math Reasoning
Write Explain why you cannot reduce the
fraction 5 .
5x - 2 _
Factor out the GCF. Simplify.
Factor out the GCF. Simplify.
Lesson 38 239