Term
When considering zero product property if one expression or variable is known to be zero, what about the other variable/expression.
D.S. TIP! 

Definition
If one is 0, the other may or may not be 0. it could be other values.
e.g. x=0
x(y3)=0.
Here since x=0, y3=0 or y3/=0 so we cant with certainty equate y3. 


Term
What can be said about 2 INTEGERS when the product is 1. 

Definition
D.S. TIP If we know 2 integers product = 1 then each integer is either 1 or +1 


Term
What are negative integers 

Definition
Numbers without fraction or decimal to left of 0 on the number line are negative integers, farther away from 0 smaller they are. 


Term
What are positive integers 

Definition
Whole numbers to the right of 0 on the number line are positive integers. Farther from 0, larger they are. 


Term

Definition
All positive integers and 0 are whole numbers 


Term
Is 0 positive or negative. 

Definition
Zero is neither positive nor negative 


Term
What is the square root of 0 

Definition


Term

Definition
0. 0 is the only number where k=k 


Term
What is a multiple of every number 

Definition


Term

Definition
1. Any number raised to 0 is 1 


Term
Which number is a factor of all numbers 

Definition


Term
What is the first prime number 

Definition
2. 0 is even and 1 is odd and not prime 


Term
What type of integer does the expression 2N represent 

Definition


Term
What type of integer does the expression 2n+1 or 2n1 represent for all integers n 

Definition


Term
What combination of odd or even integers in addition or subtraction gives an odd integer? 

Definition
Odd+Even or OddEven. All other combinations are even 


Term
What combination of odd or even integers when multiplied results in an odd integer 

Definition
Odd*odd. All other integers combination give a even integer 


Term
Given XY + Y^2 is odd. What can we say about x and y. 

Definition
X must be even and Y must be odd. Y(X+Y) = odd. so Y and (x+Y) must be odd. For x+y to be odd, x has to be odd, since y is odd. 


Term
What could be said about x,y and z if xyz=even 

Definition
IF just one variable is even, xyz = even. Can have any combination of odds (yz, xz, zy). Just one even makes it even. Similarly if all odd, it would be odd. 


Term
If x is an integer. Is x odd or even if Even/Even = X 

Definition


Term
If x is an integer. Is x odd or even if Even/Odd = X 

Definition
X must be Even. This is corollary of Even*Odd=Even => Even = Even/Odd 


Term
What is the remainder when even numbers are divided be 2 

Definition


Term
What is the remainder when odd numbers are divided by 2 

Definition


Term
What is a factor. Define using x & Y 

Definition
Considering whole numbers, If X/Y = Integer. then Y is a factor of X. 


Term
What are the largest and smallest factors of any whole number? 

Definition
The smallest is 1 and largest is the number itself. range of values for the factor is 1<=y<=x, given x/y = whole number. Note this is the same as saying X is the factor of "something" if "something"/x = integer 


Term
How to check if "something" is a multiple of x 

Definition
"something"/X should be = integer/whole number 


Term
what number has only the number itself and 1 as factors 

Definition


Term
If y is a positive integer. How many more prime factors does Y^5 and y^11 have compared to Y. 

Definition
None. A positive integer raised to another positive integer has the same number of unique prime factors as the base number 


Term
What can be said about GCF and LCM in a set of positive integers 

Definition
The LCM will be greater or equal to the largest number in the set. GCF will be greater than or equal to the smallest number in the set 


Term
What can be said about consecutive integers and the divisibility by 3 

Definition
3 consecutive integers, at least one will be divisible by 3. This can be extrapolated to 2,5 et.c 


Term
What is the factorial divisbility rule 

Definition
The product of any set of n consecutive integers is divisible by n! 


Term
Numbers that are perfect squares and perfect cubes under 1000 

Definition


Term
How can we determine if a fraction m/n is going to be terminating decimal or not 

Definition
If denominator has only factors of 2 or only factors of 5 or only both 2&5. However, be careful of what the numerator is. 


Term
What is the power of prime factors of perfect cubes 

Definition
All exponents must be multiples of 3 


Term
What are the common prime factors of x and x+1 ? 

Definition
None. 2 consecutive integers don't share any prime factors. 


Term
What is the GCF of 2 consecutive integers? 

Definition


Term
What is the units digit of x given 7,15 and 24 are factors of x ? 

Definition
0. Any number that has prime factors of at least one 2 and at least one 5 must end with at least one zero. 


Term
How do we get rid of a single term radical in the denominator 

Definition
Rationalize. x/(a)^(1/2) * (a/a)^(1/2) 


Term
For where x>1 & n>0 & both are integers.What is the relationship between x^{n }and x if n is even 

Definition


Term
For x>1 and n>1 and both integers. What is the relationship between x^{n} and x if n is odd? 

Definition


Term
For x<1 and n>0, both integers. What is the relationship between x^{n} and x if n is even? 

Definition


Term
For x<1 and n>1, both integers. What is the relationship between x^{n} and x if n is odd? 

Definition


Term
For 0<x<1 and n>0 n is integer. What is the relationship between x^{n} and x if n is even? 

Definition


Term
For 1<x<0 and n>0 n is integer. What is the relationship between x^{n} and x if n is even? 

Definition


Term
For 0<x<1 and n>1 n is integer. What is the relationship between x^{n} and x if n is odd? 

Definition


Term
For 1<x<0 and n>1 n is integer. What is the relationship between x^{n} and x if n is odd? 

Definition


Term
For x>1 and n where 0<n<1. What is the relationship between x and x^{n} 

Definition


Term
For x where 0<x<1 and n where 0<n<1. what is the relationship between x^{n} and x 

Definition


Term

Definition


Term
What is the formula for consecutive even or odd integers? 

Definition
x, (x+2), (x+4), (x+6) and so on. 


Term
0 and 1 rules when talking about multiples 

Definition
0 is multiple of all numbers and is the only number equal to all its multiples all numbers are a multiple of 1 


Term
Pattern of units digit 2^n 

Definition


Term
Pattern of units digit 3^n 

Definition


Term
Pattern of units digit 4^n 

Definition
starting n=1 46 (4 is odd power,6 is even) 


Term
Pattern of units digit 6^n 

Definition
starting n=1 all end in 6 


Term
Pattern of units digit 5^n 

Definition
Starting n=1 all powers end in 5 


Term
Pattern of units digit 7^n 

Definition


Term
Patterns of unit digit 8^n 

Definition


Term
Patterns of unit digit 9^n 

Definition
Starting n=1 91 (odd powers end 1, even powers end in 9) 


Term
Number of factors of perfect squares are 

Definition


Term
Number of factors of positive integer other than a perfect square are 

Definition


Term
If a is a factor of b is b larger than a? 

Definition
Could be. a factor of a number is lesser than OR equal to that number. therefore a is equal or less than b 

