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1. Definition
2. Example
3. Levels of usage
A. Chapters 1, 2, and 3
Mike Sebra
1- Difference of squares
steps- 1- Find the GCF among all terms
2- Put GCF outside parenthesis
3- Put each term over GCF
4- Simplify everything in parenthesis, and get factored answer
For example if you have A to the 8th minus 1 then the answer would look like this... (a4-1)(a4+1)
2- Standard form of quadratic equation
steps- 1- Grab sign pattern
2- Find factors of A and C term
3- Put choices from A and C term in bionomials. For example say if the B term is 11 and the C term is 30 the two factors would be 6x5 because they add up to 11 (6+5)
3- Greatest common factor
steps- 1- Find all factors between terms
2- Look for the highest number that is divisible by all terms
3- And thats your GCF
The GCF of 12 and 6 is 6 because it divides into both and its the highest number
4- Foil
is a method used to multiply 2 bionomials
FOIL stands for First, Outer, Inner, Last because thats the order you multiply in.(2+2)(2+4)
5- Factoring the GCF
is a process where you find the terms that multiply a number to get a product 3x3=9 which is the product of the two terms
6- Dividing bionomials by monomials
when you do this and divide by like bases you subtract the exponents
35xyz/56xyz 7(35xyz)
7- Factors
factors are numbers that divide into other numbers evenly
The factors of 10 are 1,2,5,10
8- Prime number
a prime number is a number that only is divisible by 1 and itself
An example of this is the number 11 because it has no factors besides 1 and itself
9- Divisibility
is when a number divides evenly
an example of this is 9/3 = 3 it divides evenly so 9 is divisible by 3
10- Dividing monomials
is when you divide ond term by one term
an example of this is 10/2 = 5 its just simplifying the fraction
10/2 = 5/1
Andrew Gomez
Math Vocab Ch 6
5/29/11
Factoring:
Means to pull out a common factor (number and/or variable) over a given set of numbers
Ex: 6x + 9x^2 = 3x (2 + 3x)
Rule of exponents for division:
Divide and subtract the exponents
Ex: 9x^3 / 3x = 3x^2
Prime Number:
Integer greater than 1 that has no other factors beside itself and 1
Ex: 3 (factors 3 and 1 only), 17 (factors 17 and 1 only)
Prime Factorization:
Express a positive integer as a product of its lowest factors
Ex: 18 = 2 x 3 x 3
Zero product property:
Any number multiplied by zero equals zero
Ex: 4 x 0 = 0, -7 x 0 = 0, 0 x 6.5 = 0
Multiplication Rule for fractions:
Multiply the numerators and multiply the denominators. Reduce.
Ex: 4/5 x 2/3 = 6/15 2/3 x 1/6 = 2/18 (reduces to 1/9)
Addition/Subtraction rules for fractions:
Find the lowest common denominator, change to equivalent fractions and then add/subtract the numerators. Reduce.
Ex: 2/3 + 7/9 (LCD is 9) = 6/9 + 7/9 = 13/9 = 1 4/9
Rule of exponents for products of powers:
When you multiply numbers with exponents, add the exponents
Ex: 5^3x 4 ^2 = 20^5
Factor:
A number when multiplied by another factor equals a product
Ex: 7 x 9 = 63 (7,9 are the factors)
Exponent:
Power to which a base is raised
Ex: 7^2 (2 is the exponent and means 7 x 7)
n^3 (3 is exponent and means n x n x n)
Base:
The number which an exponent operates on
Ex: 10^2 (10 is the base)
n^8 (n is the base0
Exponential Form:
an expression that uses a base and exponent
Ex: n^4