Vocab
A mathematical phrase that contains numbers and variables combined with operations
Expression
x^2+ 8
How many ways can you classify a polynomial
2
Simplify:
x+2x+2xy
3x+2xy
A number, a variables, or a of a product number and variables and with number. A polynomial with one term
monomial
Can a polynomial have a decimal in the coefficient?
yes, as long as it is not in the exponent place
How do you classify by number of terms?
Count the number of terms in the polynomial
By combining like terms
The degree of the term of the polynomial with the greatest degree
Degree of a Polynomial
Can a polynomial have a fraction as a coefficient?
yes, as long as it is not in the exponent place
Classify the polynomial, Degree and number of terms:
x^2y^2+4xy+2
4th degree, four term polynomial
Solve Vertically:
(2x^3+ 3x^2 + 2) -(3x^3 -2x^2 -4)
-x^35x^2 +6
The sum of the of the exponents of the variables in the monomial
Degree of a Monomial
What are the three properties of polynomials?
1. Constants, Variables, and exponents
2. addition, subtraction, and multiplication
3. division by numbers
How do you classify by degree?
Calculate the sum of the of the exponents in the term
Solve horizontally:
(x^2 + 2y -9) + (3x^2 - 4y +3)
4x^2- 2y - 6
The coefficient of the first term of a polynomial in standard form.
Leading Coefficient:
What can a polynomial NOT have?
1. Division by variable
2. Negative Exponents
3. Decimal exponents
4. Infinite sets (optional)
Classify the polynomial, Degree and number of terms
x^4y^3 + x^3y^2 - xy
trinomial, 7th degree
Simplify:
x^2y^2+3x^2y^2 - xy+ 3xy
4x^2y^2+3xy