# Math Alegebra

Math Study guide chapter 9, 12, and 11
Chapter 9
Section 1-Prime factorization
-Prime number is a whole number, greater then 1, whose only factors are 1 and itself
Examples- 2,3,5,7,11,13,17
-Composite numbers is a whole number greater than 1, that has more than two factors
Examples- 4, 6, 8, 10, 12, 14, 15, 16, 18
90 = 2 x 45
2 x 2 x 15
2 x 3 x 3 x 5
Section 2- factoring
12a² + 16a = 2a (6a) + 2a (8)
2a (6a + 8)
Section 3- factoring
F.O.I.L = First, outside, inside, and last
X² + 7x + 12
(x+4)(x+3)

Section 4- factoring
5x² + 27x + 10
(x+5)(5x+2)

4x² + 24x+ 32
4(x² + 6x +8)
4(x+4)(x+2)
Section 5, 6- the four special cases
(x+y)² = x² + 2xy + y² = (x+y)(x+y)
(x-y)² = (x-y)(x-y)= x² - 2xy+ y²
(x-y)(x+y) = x² - y²
Prime = x² + y²

Chapter 12
15 =   5
12     4

X² -2x-15 =   (x+3)(x-5) =   x-5
X²-x-12 (x+3)(x-4)     x-4
When you have variables in the denominators, you must make sure the denominator in not 0. These are the excluded values.
2x-10
x² -25   =   (x-5)(x+5) excluded values are 5 and -5
Section 3- multiplying national expressions
To multiply rational numbers expressed as fractions, you multiply numerators and multiply denominators. You can use this same method to multiply rational expressions.
When you multiply fraction that involve units of measure, you can divide by the units in the same way that you divide by variables

Section 4- dividing rational expressions
Recall that to divide rational numbers expressed as fractions you multiply by the reciprocal of the divisor. You can use this same method to divide rational expressions.
5x² ÷ 10x³ =   5x² • 21
7 21   7 10x³
Section 7- rational expressions with unlike denominators
Least common multiple (LCM) is the least number that is a common multiple of two or more numbers.
Denominators:
12bc² + 32 b²c= 96b³c³
Section 8- mixed expressions and complex expressions
Changing mixed expressions to...