math vocab

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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


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