# Study sets matching "polynomials chapter 5"

monomial

degree of a monomial

polynomial

polynomial function

Is a real number, a variable, or a product of a real number an…

The degree of a monomial in one variable is the exponent of th…

a monomial or a sum of monomials

...

monomial

Is a real number, a variable, or a product of a real number an…

degree of a monomial

The degree of a monomial in one variable is the exponent of th…

monomial

degree of a monomial

polynomial

degree of a polynomial

Is a real number, a variable, or a product of a real number an…

The degree of a monomial in one variable is the exponent of th…

a monomial or a sum of monomials

The degree of a polynomial in one variable is the greatest deg…

monomial

Is a real number, a variable, or a product of a real number an…

degree of a monomial

The degree of a monomial in one variable is the exponent of th…

Monomial

Degree of a Monomial

Polynomial

Degree of a Polynomial

a real number, a variable, or a product of a real number and o…

the exponent of the variable

a monomial or a sum of monomials

the greatest degree among its monomial terms

Monomial

a real number, a variable, or a product of a real number and o…

Degree of a Monomial

the exponent of the variable

Positive Integral Exponents

Negative Integral Exponents

Zero Exponent

Product Rule of Exponents

If x is a nonzero real number, and n is a positive integer, th…

If x is a nonzero real number, and n is a negative integer, th…

If a is any nonzero real number, then a⁰=1

If m and n are integers, and a=0, then aᵐ × aⁿ = aᵐ⁺ⁿ

Positive Integral Exponents

If x is a nonzero real number, and n is a positive integer, th…

Negative Integral Exponents

If x is a nonzero real number, and n is a negative integer, th…

Product Rule

Quotient Rule

Power of a Power

Power of a Product

When multiplying exponents with the same base, keep the base a…

When dividing exponents with the same base, keep the base and…

To raise a power to a power, multiply the exponents

Each base is raised to the power

Product Rule

When multiplying exponents with the same base, keep the base a…

Quotient Rule

When dividing exponents with the same base, keep the base and…

Polynomial/Polynomial Function

Synthetic Substitution

End Behavior

Factor Completely

A polynomial is a monomial or a sum of monomials. A polynomial…

Another way to evaluate a polynomial function is to use synthe…

The end behavior of a function's graph os the behavior of the…

A factorable polynomial with integer coefficients is factored…

Polynomial/Polynomial Function

A polynomial is a monomial or a sum of monomials. A polynomial…

Synthetic Substitution

Another way to evaluate a polynomial function is to use synthe…

Leading Coefficient

Constant Term

Degree

End Behavior

Coefficient in front of the x-variable with has the highest po…

A term that has no variable part, such as -4 or 2

The degree of a polynomial corresponds to the highest power on…

The behavior of the graph of a function as x approaches positi…

Leading Coefficient

Coefficient in front of the x-variable with has the highest po…

Constant Term

A term that has no variable part, such as -4 or 2

End behavior

Local Maximum

Local Minimum

Zeros

Describes the direction of the y-values as x goes to positive…

A peak in the y-values of the graph of the function, but not t…

A low in the y-values of the graph of the function, but not th…

Where the graph of the function touches or crosses the y-axis.

End behavior

Describes the direction of the y-values as x goes to positive…

Local Maximum

A peak in the y-values of the graph of the function, but not t…

Products of Exponents... Product of Powers

Products of Exponents... Power of a Power

Products of Exponents... Power of a Product

Products of Exponents... Negative Exponent

a ⁿ ₀ aⁿ = a ⁿ⁺ⁿ

(a ⁿ )ⁿ = a ⁿⁿ

(ab) ⁿ = a ⁿb ⁿ

a⁻ⁿ = 1/aⁿ , a ≠ 0

Products of Exponents... Product of Powers

a ⁿ ₀ aⁿ = a ⁿ⁺ⁿ

Products of Exponents... Power of a Power

(a ⁿ )ⁿ = a ⁿⁿ

monomial

Degree of the Monomial

Rule For Multiplying Exponential Expres…

Rule For Dividing Exponential Expressio…

a number, a variable, or a product of a number and variables.

sum of the exponents of the variables

If same base and multiplying= add exponents

If same base and dividing= subtract the exponents

monomial

a number, a variable, or a product of a number and variables.

Degree of the Monomial

sum of the exponents of the variables

polynomial

monomials

1 term

2 terms

A sum and or difference of one or more monomial.

a term made of the product of one or more contants and/or vari…

monomial ex: 3x

binomial ex: 5x(2)=7

polynomial

A sum and or difference of one or more monomial.

monomials

a term made of the product of one or more contants and/or vari…

When dividing exponential expressions w…

In the zero-exponent rule, if "b" is an…

If "a" and "b" are real numbers and "b"…

To divide monomials, _____ and then ___…

subtract the exponent in the denominator from the exponent in…

1

aⁿ/bⁿ

divide the coefficients... divide the variables... the quotient ru…

When dividing exponential expressions w…

subtract the exponent in the denominator from the exponent in…

In the zero-exponent rule, if "b" is an…

1

When multiplying exponential expression…

When a product is raised to a power, __…

To multiply monomials with the same var…

To multiply a monomial and polynomial,…

add the exponents... the exponent of the common base... b^m+n

raise each factor to the power... aⁿbⁿ

multiply the coefficients and then multiply the variables... Kee…

use the distributive property to multiply each term of the pol…

When multiplying exponential expression…

add the exponents... the exponent of the common base... b^m+n

When a product is raised to a power, __…

raise each factor to the power... aⁿbⁿ

Binomial Theorem

Conjugates

Degree of a Polynomial

Difference of Cubes

Binomials of the form a + √b and a - √b.

The greatest of the degrees of its terms after it has been sim…

Binomial Theorem

Conjugates

Binomials of the form a + √b and a - √b.

when multiplying two numbers with expon…

when a number with an exponent has an e…

when two variables are being multiplied…

when the same variable with different e…

multiply coeffients (not bases) and add exponents... x^m+n

multiply exponents, if there is a coefficient, multiply that b…

multiply the variables by the exponent... x^m y^m

subtract the exponents... x^m-n

when multiplying two numbers with expon…

multiply coeffients (not bases) and add exponents... x^m+n

when a number with an exponent has an e…

multiply exponents, if there is a coefficient, multiply that b…

degree of a polynomial

depressed polynomial

end behavior

extrema

The degree of the monomial with the greatest degree

A polynomial that has a degree one less than the original poly…

The behavior of the graph of f(x) as x approaches positive inf…

The maximum and minimum values of a polynomial function

degree of a polynomial

The degree of the monomial with the greatest degree

depressed polynomial

A polynomial that has a degree one less than the original poly…