Alegebra

Question 1

natural numbers (1)

Answer 1

1,2,3,… aka counting numbers

all positive, whole numbers

Question 2

whole numbers (1)

Answer 2

natural numbers starting at 0

Question 3

integers (1)

Answer 3

combine negative numbers with whole number

Question 4

rational number (1)

Answer 4

quotient of two integers

includes repeating and terminating decimals

Question 5

irrational numbers (1)

Answer 5

cannot be expressed as quotient of two integers

includes ongoing decimals

Question 6

open interval (1)

Answer 6

*interval - (a,b)
*set-building - {x|a<b}
hollow/open dots

Question 7

closed interval (1)

Answer 7

*interval - [a,b]
*set-builder - {x|a<=b}
closed/filled dots

Question 8

half-open intervals (1)

Answer 8

*interval - (a,b]
*set-builder - {x|a<=b}
hollow a, full b

Question 9

open infinite intervals (1)

Answer 9

• interval - (a,infinity)

* set-builder - {x|x>a}

Question 10

sets - union and intersection (1)

Answer 10

• union - elements when you COMBINE sets (U) - like a bucket

* intersection - elements common in both (Upside-down U) like “N”. Empty set is 0.

Question 11

absolute value (1)

Answer 11

distance between number and 0

|n|

Question 12

opposite (1)

Answer 12

x + opposite = 0

Question 13

multiply fractions (1)

Answer 13

top and bottom straight across

*don’t need common denominator

Question 14

reciprocal (1_

Answer 14

x * reciprocal = 1

flip fraction, keep sign

Question 15

defined vs undefined (1)

Answer 15

a/b and a and b are real numbers and b is not 0

Question 16

dividing fractions (1)

Answer 16

flip on and multiply straight across

*no need for common denominator

Question 17

negative base w/exponent (1)

Answer 17

negative stays

*in parenthesis, negative is multiplied

Question 18

order of ops (1)

Answer 18

• parenthesis/groups
• exponents
• multiply/divide
• add/subtract

Question 19

negative exponents (2)

Answer 19

flip to below fraction

x^-4 = x^-4/1 = 1/x^4

Question 20

FOIL method (2)

Answer 20

First, Outer, Inner, Last

Question 21

factoring polynomials by grouping (2)

Answer 21

1 identify
2 group
3 factor
4 identify
5 factor again

Question 22

factoring trinomial a not equal to 1 (2)

Answer 22

ax^2+bx+c

1. a*c
2. find 2 numbers that multiply for that value and add for b
3. rewrite b with these values
4. group
5. simplify and regroup

Question 23

long division with polynomials (2)

Answer 23

*insert coefficient 0 where needed (0x)
1 divide by first item under by first item over
2 multiply first answer by items over
3 subtract and carry down
4 do again until done
5 item under is remainder
6 answer above times items over plus remainder equals polynomial

Question 24

factoring binomials with 2 squares (ch2)

Answer 24

a^2-b^2 = (a+b)(a-b)

Question 25

factoring trinomials with squares (ch2)

Answer 25

a^2 + 2ab +b^2 = (a+b)^2

Question 26

rational expression (2)

Answer 26

P/O where O<>0

Question 27

multiply polynomials using special product formula (2)

Answer 27

(x-a)^2 = x^2-2ax+a^2