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Understanding Polynomials

6.1.1 Understanding Polynomials

6.1.1 • Understanding Polynomials

Warm Up

A monomial is an algebraic expression with exactly one term: 5x25x2

A binomial is an algebraic expression with exactly two terms: 5x2+6y35x2+6y3

A trinomial is an algebraic expression with exactly three terms: 5x2+6y3−7c5x2+6y3−7c

Monomials, binomials, and trinomials are all different types of polynomials. A polynomial is a monomial or two or more monomials combined by addition or subtraction.

The degree of a polynomial is the highest degree of all its terms.

Examine the following expressions and use them to answer questions 1 – 6.

x 2 x 2
c + 4 c + 4
m n m n
8 d 2 + 3 e − g 8 d 2 + 3 e − g
b − h b − h
15 15
n 2 − 7 f + a b n 2 − 7 f + a b
z z
A collection of algebraic expressions, demonstrating various forms and complexities.
1.

Which of the polynomials listed above are monomials?

There are four answers: x 2 x 2 , 15 15 , z z , m n m n

2.

Which of the polynomials listed above are binomials?

There are two answers: c + 4 c + 4 and b − h b − h

3.

Which of the polynomials listed above are trinomials?

There are two answers: 8 d 2 + 3 e − g 8 d 2 + 3 e − g , n 2 − 7 f + a b n 2 − 7 f + a b

4.

Which of the polynomials listed above have a degree of 0?

There is only one answer: 15 15

5.

Which of the polynomials listed above have a degree of 1?

There are three answers: c + 4 c + 4 , b − h b − h and z z

6.

Which of the polynomials listed above have a degree of 2?

There are four answers: x 2 x 2 , 8 d 2 + 3 e − g 8 d 2 + 3 e − g , n 2 − 7 f + a b n 2 − 7 f + a b , and m n m n