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Why is this concept useful?: Polynomials are useful to model complex relationships. They are the building blocks of Algebraic concepts.
Where does this concept fit into the curriculum?: Algebra 1

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There is important vocabulary to understand when referring to polynomials.

Monomial: a number, a variable or a product of a number and one or more variables.

Degree of a Monomial: the sum of the exponents.

Term: either a single number or variable, or numbers and variables multiplied together.

Constant Term: the number monomial in a polynomial.

Degree of a Polynomial: the sum of the exponents in the monomial of the highest degree.

Leading Coefficient: the number in front of the monomial of the highest degree.

Standard Form of a Polynomial: the monomial terms listed in decreasing degrees from left to right after combining like terms.

In the polynomial

4x^3

+

2x^2

- 3x + 1, the first three terms are monomials (

4x^3

,

2x^2

, 3x) and the number 1 is a constant.

4x^3

has a degree of 3 because of the exponent 3. It is also the degree of the polynomial because it is the term with the highest degree. It is written in Standard Form because the degrees of the monomials are decreasing.

Sample Math Problems

Question

Given the polynomial

2x^2y^3

-

4x^2y

+ xy - 2

Determine the Number of Terms, the Constant Term, the Degree of the Polynomial and the Leading Coefficient.

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Practice Math Problems

1. Given the following polynomial

2x^4

y^2

-

4x^3y

+

x^2y

- 2

Determine the Number of Terms, the Constant Term, the Degree of the Polynomial and the Leading Coefficient.

2. Combine like terms in the given set of algebra tiles and express them as a simplified polynomial.

3. Combine the like terms and give the answer in Standard Form.

(

2x^2

+ 2x + 8) + (

x^2

+ 3x + 12)

4. Combine the like terms and give the answer in Standard Form

(

5x^2

+ 7x - 4) - (

3x^2

- 3x + 4)

Solution

Number of Terms = 4 (the number of monomials in the polynomial)

Constant Term = -2 (the monomial that is a number only)

Degree of the Polynomial = 5th degree. (To find the degree, add the exponents of each term. The one with the highest sum indicates the degree of the polynomial)

Leading Coefficient = 2 (the number in front of the monomial indicating the Degree of the Polynomial)

Question

Combine like terms in the given set of algebra tiles and express them as a simplified polynomial.

KaTeX can only parse string typed expression

The number of each algebra tile is the coefficient for each monomial. Write the monomials in the Standard Form of a Polynomial.

Solution

3x^2

+

4y^2

+3x + 8y + 2

Question

Combine the like terms and give the answer in Standard Form.

Solution

(

5x^2

+ 3x + 7) + (

2x^2

+ x + 3) =

7x^2

+ 4x + 10

Question

Combine the like terms and give the answer in Standard Form

Solution

(

3x^2

+ 2x - 4) - (

x^2

- 4x + 8) =

2x^2

+ 6x - 12

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Algebra Worksheets

Polynomials

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Tossing a Coin

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Math Tutoring to Boost Your Child’s Math Skills & Scores by 90% in Just 3 Months – Guaranteed!

Sample Math Problems

Download FREE Math Resources

8 Math Hacks and Tricks to Turn Your 'Okay' Math Student Into a Math Champion!

How to Make Sure Your Child is Highly Successful and Becomes a Millionaire

Practice Math Problems