XXXXVI Uses of Algebraic Factoring

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XXXXVIUses of Algebraic Factoring

• To Solve factorable equations of degrees (powers)
  greater than one.
• Ex 1) 2x2 8 0
• 2(x2 4) 0
• 2(x 2)(x 2) 0
• SS x x 2
• or
• SS x x 2, x -2

1st degree equations are called linear
equations. 2nd degree equations are called
quadratic equations. 3rd degree equations are
called cubic equations 4th degree equations are
known as quartic equations. 5th degree equations
are called quintic equations.
An Equation will yield as many answers as the
highest degree of the equation. In this case, the
highest power is two, and that is how many
answers will be in the solution set
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XXXXVIUses of Algebraic Factoring (Continued)
Ex 2) 2x3 3x2 2x 3 0 x2(2x -3)
(2x 3) (x2 1)(2x 3) 0 (x 1)(x
1)(2x 3) 0 2x 3 0 x 1 0 x 1
0 2x 3 x 1 x -1 2 2 x
3 SS x x 1, x 2
Notice that this is a cubic equation, which means
it will yield three answers.
3 2
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XXXXVIUses of Algebraic Factoring (Continued)
Ex 3) x4 13x2 36 0 (x2 4)(x2 9)
0 - 4x2 - 9x2 (x 2)(x 2)(x 3)(x
3) 0 x 2 0 x 2 0 x 3 0 x
3 0 x 2 x -2 x 3 x
-3 SS x x 2, x 3
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XXXXVIUses of Algebraic Factoring (Continued)
b) To Reduce Algebraic Fractions Ex 1) x2 2x
1 3x2 3 (x 1)(x 1) 3(x
1)(x 1) (x 1) 3(x 1)

• Rules
• Prime factorize tops and
  bottoms.
• Cancel Like Factors.

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XXXXVIUses of Algebraic Factoring (Continued)
Ex 2) 4 b b2 5b 4 4
b (b 4)(b 1) -1 _ (b
1) Or 1 _ 1 b
b 4 ? 4 b Opposites will always yield -1 Just
as 6 -6 Will yield -1
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XXXXVIUses of Algebraic Factoring (Continued)
c) Multiplying fractions Ex 1) 11m 14 _
21 55m3 11m 7 2
_ 7 3 11 5 m m m
2_ 15m2

• Rules
• Prime factorize tops and bottoms.
• 2)Cancel any top with a like bottom.
• 3)Move left to right when solving.

.
.
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XXXXVIUses of Algebraic Factoring (Continued)
Ex 2) p2 p 6 2p2 5p 3 3p 9
p2 3p (p 2)(p 3) (2p 1)(p 3) 3(p
3) p(p 3) (p 2)(2p 1) 3p
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XXXXVIUses of Algebraic Factoring (Continued)
d) Division of Fractions Ex 1) x2 x 6
_ x2 25 _ 2x2 9x
10 2x2 15x 25 x2 x 6 _ 2x2
15x 25 _ 2x2 9x 10 x2
25 (x 2)(x 3) (2x 5)(x 5) (2x
5)(x 2) (x 5)(x 5) x
3 x 5

• Rules
• Invert back or bottom fraction.
• 2)Prime factorize tops and bottoms.
• 3)Cancel any top with a like bottom.
• 4)Move left to right when solving.

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XXXXVIUses of Algebraic Factoring (Continued)
Ex 2) 6x3 48y6 8(x 2y2) 6(x3
8y6) 8(x 2y2) 6(x 2y2)(x2 2xy2
4y4) 8(x 2y2) 3(x2 2xy2
4y4) 4
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XXXXVIUses of Algebraic Factoring (Continued)
e) Addition and Subtraction of Fractions Ex
1) 2x _ x 1 _ 3x2
27 5x2 11x 12 2x _ x
1 _ 3(x 3)(x 3) (5x 4)(x
3) GET JEALOUS (5x 4)(2x) 3(x 3)(x
1) 3(5x 4)(x 3)(x 3) 13x2 20x
9 3(5x 4)(x 3)(x 3)

• Rules to get LCD
• Prime factorize Denominator only
• Get Jealous