Naming Polynomials by Degree and Number of Terms

CLASSIFYING POLYNOMIALS

A POLYNOMIAL can be classified by its number of terms and by its degree.

NUMBER OF TERMS

• A polynomial with 1 term is a MONOMIAL.

• A polynomial with 2 terms is a BINOMIAL.

• A polynomial with 3 terms is a TRINOMIAL.

• A polynomial with more than 3 terms is called a POLYNOMIAL.

DEGREE OF A MONOMIAL

DEGREE OF A POLYNOMIAL

• The degree of a polynomial is the highest exponent.

• Polynomials must be written in standard form before classifying by degree.

• A polynomial with one variable is written in standard form when its terms are written in descending order by degree.

The highest exponent is the 2 and there are 3 terms. 

This is a QUADRATIC TRINOMIAL.

The highest exponent is the 4 and there are 2 terms.

This is a QUARTIC BINOMIAL.

While it appears there is no exponent, the x has an understood exponent of 1 and there are 2 terms.

Therefore, this is a LINEAR BINOMIAL.

Since both variables are part of the same term, we must add their exponents together to determine the degree.   

2 + 5 = 7 so this is a 7TH DEGREE MONOMIAL.

Multiple Choice

Classify the polynomial by its number of terms.

$$7x^3+5x^2+1$$  

• MONOMIAL

• BINOMIAL

• TRINOMIAL

• POLYNOMIAL

Multiple Choice

Classify the polynomial by its number of terms.

$$6y^5+9y^2-3y+8$$  

• MONOMIAL

• BINOMIAL

• TRINOMIAL

• POLYNOMIAL

Multiple Choice

Classify the polynomial by its number of terms.

$$8x-4$$  

• MONOMIAL

• BINOMIAL

• TRINOMIAL

• POLYNOMIAL

Multiple Choice

Classify the polynomial by its number of terms.

$$9x^2y+3$$  

• MONOMIAL

• BINOMIAL

• TRINOMIAL

• POLYNOMIAL

Multiple Choice

Classify the polynomial by its number of terms.

$$12x^2$$  

• MONOMIAL

• BINOMIAL

• TRINOMIAL

• POLYNOMIAL

Multiple Choice

Classify the polynomial by its degree.

$$7x^3+5x^2+1$$  

• CONSTANT

• LINEAR

• QUADRATIC

• CUBIC

• QUARTIC

Multiple Choice

Classify the polynomial by its degree.

$$6y^5+9y^2-3y+8$$  

• LINEAR

• CUBIC

• QUADRATIC

• QUARTIC

• QUINTIC

Multiple Choice

Classify the polynomial by its degree.

$$8x-4$$  

• CONSTANT

• LINEAR

• QUADRATIC

• CUBIC

• QUARTIC

Multiple Choice

Classify the polynomial by its degree.

$$9x^2y+3$$  

• CONSTANT

• LINEAR

• QUADRATIC

• CUBIC

• QUARTIC

Multiple Choice

Classify the polynomial by its degree.

$$12x^2$$  

• LINEAR

• QUADRATIC

• CUBIC

• QUARTIC

• QUINTIC

Multiple Select

Classify this polynomial by degree and classification.

$$5x^2-3x+2$$  

• Quadratic

• Cubic

• Binomial

• Trinomial

Multiple Select

Classify this polynomial by degree and classification.

$$4x+10$$  

• Quadratic

• Linear

• Binomial

• Trinomial

Multiple Select

Classify this polynomial by degree and classification.

$$6x^3$$  

• Cubic

• Linear

• Monomial

• Trinomial

Multiple Select

Classify this polynomial by degree and classification.

$$5x^3+2x^2-5x+9$$  

• Cubic

• Linear

• Monomial

• Polynomial

Multiple Choice

Classify this polynomial by its degree and number of terms: x² + 6

• Linear polynomial

• Quadratic trinomial

• Quadratic binomial

• Cubic binomial

Ordering Polynomials

Multiple Select

Which of the following polynomials are in "standard form" or the correct order

• $$3x^8+2x^5-9$$

• $$10+8p^2-6p$$

• $$4a^2-14$$

• $$5y^8+5x^7+5x^6$$

• $$144-x^2$$

Multiple Choice

What is the standard form of the polynomial,

9x² + 5x + 27 + 2x³

• 27 + 5x + 9x² + 2x³

• 9x² + 5x + 2x³ + 27

• 9x² + 5x + 27 + 2x³

• 2x³ + 9x² + 5x + 27

Multiple Choice

What is the standard form of the polynomial,

7x - 125 - 6x⁴ + 14x²

• 125 + 7x - 14x² +6x⁴

• 6x⁴ -14x² - 7x +125

• 125 + 14x² + 7x - 6x⁴

• -6x⁴+ 14x² + 7x - 125

Multiple Choice

Which one of these is in standard form?

Multiple Choice

Put this expressions in Standard Form.
5y - 9 - 2y²

• -2y² + 5y - 9

• 2y² - 5y - 9

• 5y - 9 - 2y²

• -9 - 5y - 2y²