Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis; Jay Abramson; Sharon North; Amy Baldwin; Alyssa Howell

Activity

A monomial is an algebraic expression with exactly one term: $5 x^{2}$

A binomial is an algebraic expression with exactly two terms: $5 x^{2} + 6 y^{3}$

A trinomial is an algebraic expression with exactly three terms: $5 x^{2} + 6 y^{3} - 7 c$

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.

Link to Learning

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

x^{2}

c + 4

m n

8 d^{2} + 3 e - g

b - h

15

n^{2} - 7 f + a b

z

1.

Which of the polynomials listed above are monomials?

There are four answers: $x^{2}$ , $15$ , $z$ , $m n$

2.

Which of the polynomials listed above are binomials?

There are two answers: $c + 4$ and $b - h$

3.

Which of the polynomials listed above are trinomials?

There are two answers: $8 d^{2} + 3 e - g$ , $n^{2} - 7 f + a b$

4.

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

There is only one answer: $15$

5.

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

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

6.

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

There are four answers: $x^{2}$ , $8 d^{2} + 3 e - g$ , $n^{2} - 7 f + a b$ , and $m n$

6.1.1 Understanding Polynomials

Activity