Polynomials

Vocab

100

A mathematical phrase that contains numbers and variables combined with operations

Expression

200

A number, a variables, or a of a product number and variables and with number. A polynomial with one term

monomial

300

 The degree of the term of the polynomial with the greatest degree

Degree of a Polynomial

400

The sum of the of the exponents of the variables in the monomial

Degree of a Monomial

500

The coefficient of the first term of a polynomial in standard form.

Leading Coefficient:

Polynomials: dos and don't's

100

Is this a polynomial? why?

x^2+ 8

Yes, there are no negative exponents, decimal exponents, or variables in the denominator 

200

Can a polynomial have a decimal in the coefficient?

yes, as long as it is not in the exponent place

300

Can a polynomial have a fraction as a coefficient?

yes, as long as it is not in the exponent place

400

What are the three properties of polynomials?

1. Constants, Variables, and exponents

2. addition, subtraction, and multiplication

3. division by numbers

500

What can a polynomial NOT have?

1. Division by variable

2. Negative Exponents

3. Decimal exponents

4. Infinite sets (optional)

Classification

100

How many ways can you classify a polynomial

2

200

How do you classify by number of terms?

Count the number of terms in the polynomial

300

Classify the polynomial, Degree and number of terms:

x^2y^2+4xy+2

4th degree, four term polynomial

400

How do you classify by degree?

Calculate the sum of the of the exponents in the term

500

Classify the polynomial, Degree and number of terms

x^4y^3 + x^3y^2 - xy

trinomial, 7th degree

Simplification

100

Simplify: 

x+2x+2xy

3x+2xy

200

How do you simplify an expression?

By combining like terms

300

Solve Vertically:

(2x^3+ 3x^2 + 2) -(3x^3 -2x^2 -4)

-x^35x^2 +6

400

Solve horizontally:

(x^2 + 2y -9) + (3x^2 - 4y +3)

4x^2- 2y - 6

500

Simplify:

x^2y^2+3x^2y^2 - xy+ 3xy

4x^2y^2+3xy