math vocab
term
either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs.
perfect square trinomial
(a + b)2= a2 + 2ab + b2 (a - b)2 = a2 - 2ab + b2
power rule for exponents
(am)n = amn, this says that to raise a power to a power you need to multiply the exponents.
factor by grouping
1.Step 1: Group the first two terms together and then the last two terms together. 2.Step 2: Factor out a GCF from each separate binomial. 3.Step 3: Factor out the common binomial.
end behavior of a polynomial
A positive cubic enters the graph at the bottom, down on the left, and exits the graph at the top, up on the right. Since the leading coefficient of this odd-degree polynomial is positive, then its end-behavior is going to mimic a positive cubic. "Down" on the left and "up" on the right.
difference of perfect squares
Both x^2 and 9 are perfect squares. Since subtraction is occurring between these squares, this expression is the difference of two squares. What times itself will give x2 ? The answer is x. What times itself will give 9 ? The answer is 3. Answer: (x + 3) (x - 3)
degree of a term
For a term with one variable, the ____________ is the variable's exponent. With more than one variable, the ____________ is the sum of the exponents of the variables.
zero of a polynomial
It is a solution to the polynomial equation, P(x) = 0. It is that value of x that makes the polynomial equal to 0. It is traditional to speak of a root of a polynomial. Of a function in general, we speak of a zero.
root of a polynomial
When we see a graph of a polynomial, real roots are x-intercepts of the graph of f(x).
constant
a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are _____________
coefficient
a numerical or constant quantity placed before and multiplying the variable in an algebraic expression
zero rule for exponents
a^0 = 1, this says that anything raised to the zero power is 1.
sum of two cubes
a^3 + b^3 = (a + b)(a2 - ab + b2)
difference of two cubes
a^3 - b^3 = (a - b)(a2 + ab + b2)
monomial
algebraic expression consisting of one term
trinomial
algebraic expression consisting of three terms
binomial
an algebraic expression of the sum or the difference of two terms, consisting of two terms
polynomial
an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable
greatest common factor
is the greatest factor that divides two numbers. To find the __________of two numbers: List the prime factors of each number. Multiply those factors both numbers have in common.
degree of a polynomial
is the highest degree of its terms when the polynomial is expressed in its canonical form consisting of a linear combination of monomials.
negative exponent rule
negative exponents in the numerator get moved to the denominator and become positive exponents. Negative exponents in the denominator get moved to the numerator and become positive exponents.
descending order
numbers arranged from largest to smallest numbers, A polynomial with its terms simplified and written so that the powers of the variables are in order from largest to smallest is said to be in___________
factoring
process of finding the factors, It is like "splitting" an expression into a multiplication of simpler expressions.
like terms
terms that contain the same variables raised to the same power. Only the numerical coefficients are different. In an expression, only _________ can be combined. We combine __________ to shorten and simplify algebraic expressions ex: 5x + 2x
quotient rule for exponents
that to divide two exponents with the same base, you keep the base and subtract the powers.
FOIL
the standard method of multiplying two binomials
power of a product
when multiplying two powers that have the same base, you can add the exponents.
product rule for exponents
when multiplying two powers that have the same base, you can add the exponents.
prime polynomial
when the factors of an algebraic expression are only one and itself