# THOMP ALG 5

## 33 terms

### power of a product

to raise a product, raise each factor of the product to that power

### power of a quotient

to raise a quotient to a power, raise the numerator and denominator to that power.

### power rule for exponents

to raise an exponential to a power, keep the base and multiply the exponents

### base

out of xⁿ, it's the x

### exponent

out of xⁿ, it's the n

### product rule of exponents

to multiply exponential expressions with the same base, keep the common base and add the exponents

### scientific notation

provides a compact way of writing very large or very small numbers

### exponent expression

out of xⁿ, it's the xn

### zero exponent

a nonzero based raise to the 0 power is 1

### negative exponent

x ⁻ⁿ, is the reciprocal of xⁿ

### quotient rule for exponents

to divide exponential expressions with the same base, keep the common base and subtract the exponents

### fractions to negative powers

to raise a fraction to the negative ⁿth power, invert the fraction

### standard notation

the long drawn out numbers. normal way of writing them

### constant term

the term contains only one number (no variable)

### term

number or product of a number and a variable raised to a power

### numerical coefficient

numerical factor of a term

### polynomial

single term or sum of terms in which all variables have whole number exponents. no variable in denominator

### degree of polynomial

same as the degree of the term in the polynomial with largest degree

### polynomial function

function whose equation is defined by a polynomail in one variable

x²+ 2xy + y²

x² -2xy +y²

x²-y²

### factor

the number that divides a second number exactly,

### prime factored form

number broken down into prime factors

### GCF

list of integers in the largest common factor

### factor by grouping

group the terms of the polynomial so that each group has a common factor, factor out the common factor from each group, factor out the resulting common factor.

### perfect square trinomails

trinomials that are squares of a binomial

### perfect interger squares

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400

x²-y²

x³ +y³

x³ - y³

### x³ +y³

(x + y) (x²- xy+y²)

### x³ - y³

(x - y) (x²+xy+y²)