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

Section 2- simplify radial expressions

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...