Algebra Flashcards
polynomial
an expression containing constants, variables, and exponents but never with negative exponents or with division by a variable.
fractional exponent
a fractional exponent such as 9 raised to the 1/n power
means to take the n-th root of the whole number (9)
So… if we set n = 2 then
9 raised to the 1/2 power = 3
negative exponent
how many times to divide 1 by the number being raised to that power
So that 8 to -1 power is 1 /8 = 0.125
So that 5 to -3 power is 1 / 5 / 5 /5 or 1 / 5 cubed (125)
5 to -3 power = 1/125 = 0.008
an expression
a combination numbers and symbols (such as parenthesis and +- = etc or letters that are variables such x and y or a and b or i)
These combinations are formed according to a set of operations or rules.
Expressions can be simplified by reducing them.
coefficient
a number used to multiply a variable
Operator
A symbol that shows an operation (what is to be done by one value to another value)
constant
a number by itself
monomial, binomial, trinomia
names of the polynomials with 1, 2, or 3 terms respectivey
like terms
terms whose variables and their exponents are the same but whose coefficiemts may vary.
1/3xy and -2xy and 6xy have different coefficients but corresponding variables with their corresponding exponents
exponent
indicates how many times to use that number in multiplication (times itself)
exponent of zero
a non-zero number raised to the zero exponent (the zero power) is 1
zero raised to zero exponent
Is indeterminate … can be either zero or 1
reciprocal
to divide one by a number
reciprocal of a fraction
turn the fraction upside down, flip it
reciprocal of a variable can also be written as
The negative exponent of a number
1/x = x raised to the -1 power
proportion
two ratios (or also written as fractions) are equal
percentage
a ratio of parts per 100
directly proportional
as one increases the other increases at same rate
symbol - not infinity symbol (♾) but infinity with the right end open (oc)
constant of proportionality
the value that relates two numbers in proportion … often called “the constant”
inversely proportional
One value decreases at the same rate the other value is increasing
proportional to (a multiple)
Constant proportion to the square or cube or any other function
eg distance is proportional to the square of the time it takes an object to fall
d = distance k = constant proportion t = time
d = k(t)squared
inverse square (proportion)
when one value decreases as the inverse of the square of the other value
eg light intensity decreases by the inverse sqaure of distance
Expanding is the opposite of
Factoring is the opposite of
difference of squares formula
(a+b)(a-b) = a(squared)-b(squared)
a plus b times a minus b equals aSquared minus bSquared
factorial identities
there are 7 most useful factoring formulas - find a math deck that has them and study it
rational expression
a ratio of two polynomials
in other words a fraction with one polynomial in the numerator and another polynomial in the denominator
x(squared) + 5 / x + 2
roots of a rational expression
the points where the expression is equal to zero
the conjugate of a binomial
A binomial with its sign changed (either plus to minus or minus to plus)
