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Level 401

Exponents & Polynomials


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zero exponent
It's value is always 1.
negative exponent
Means to write the reciprocal of the base and use a positive exponent
Scientific notation
where a number is written into 2 parts first just the digits (with decimal point after first digit) followed by ×10 to a power
Product of Powers Property
Example: 2² * 2³ = 2²⁺³
Power of a Power Property
I <i>a</i> is any nonzero real numbers and <i>n</i> is an integer, then <color red>(ab)ⁿ = aⁿbⁿ</color>.
Power of a Product Property
(ab)^x = a^x * b^x
Quotient of Powers Property
to divide powers WITH THE SAME NON ZERO BASE, subtract the exponents a^m/a^n = a^m-n
Positive Power of a Quotient Property
If <i>a</i> and <i>b</i> are nonzero real numbers and <i>n</i> is a positive integer, then <color red>(a/b)ⁿ = aⁿ/bⁿ</color>.
Negative Power of a Quotient Property
If <i>a</i> and <i>b</i> are nonzero real numbers and <i>n</i> is a positive integer, then <color red>(a/b)⁻ⁿ = (b/a)ⁿ = bⁿ/aⁿ</color>.
index
In the radical <i>ⁿ√x</i>, which represents the <i>n</i>th root of <i>x</i>, <i>n</i> is the index. In the radical √x, the index is understood to be 2.
<i>n</i>th root
The <i>n</i>th root of a number <i>a</i>, written as ⁿ√a or <i>a</i> ^(1/n), is a number that is equal to <i>a</i> when it is raised to the <i>n</i>th power.
b^(1/n)
A number raised to the power of 1/n is equal to the <i>n</i>th root of that number.
b^(m/n)
If <i>b</i> > 1 and <i>m</i> and <i>n</i> are integers, where <i>m</i> ≥ 1 and <i>n</i> ≥ 2, then b ^(m/n) = (ⁿ√b)^m = ⁿ√b^m.
monomial
a number or a product of numbers and variables with exponents that are whole numbers
Degree of a monomial
the sum of the exponents of the variables
polynomial
A monomial or sum of monomials
Degree of a polynomial
the degree of the term in the polynomial that has the highest degree
standard form of a polynomial
is written with terms from highest to lowest degree
leading coefficient
The coefficient of the term with the highest degree
quadratic polynomial
A polynomial of degree 2.
cubic polynomial
A polynomial of degree 3.
trinomial
A polynomial with 3 terms
binomial
A polynomial with two terms
root
A root of a polynomial in one variable is a value of the variable for which the polynomial is equal 0.
FOIL
To convert Factored Form to Standard Form you must
perfect-square trinomial
A trinomial whose factored form is the square of a binomial. A perfect-square trinomial has the form <i>a² − 2ab + b²</i> or <i>a² + 2ab + b²</i>.
difference of two squares
A polynomial of the form <i>a² − b²</i>, which may be written as the product <i>(a + b)(a − b)</i>.