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Algebra has many different new words that you will come to learn and understand. Words such as variables, exponents, coefficients, monomials, binomials, trinomials and polynomials. For this quiz, we are going to focus on the following four.

A **monomial** is a mathematical number that stands alone and does not have a negative exponent. “Mono” refers to “one.” For example: 14*x*^{2} is a monomial as it stands alone. 26 is also a monomial. However, 9*x*^{-3} is not because the exponent is a negative.

A **binomial** consists of two monomials linked together with either an addition sign (+), a minus sign (-) or a multiplication sign (x). For example: 11*x*^{4} + 7*x*^{2}.

A **trinomial** consists of three monomials linked together with either an addition sign (+), a minus sign (-) or a multiplication sign (x). For example: 6*x*^{5} + 5*x*^{2} - 4.

A **polynomial** consists of multiple monomials linked together. “Poly” means many. For example: 10*x*^{4} + 3*x*^{2} - 4 + 5*x*. In truth, a binomial and a trinomial can also be referred to as polynomial but generally a polynomial will have at least four monomials or terms as each monomial or number is also referred to as a “term.”

For each of the ten algebra factors listed below, determine whether the numbers shown are a monomial, a binomial, a trinomial or a polynomial.

1.

26*x*^{3}

Monomial

Binomial

Trinomial

Polynomial

When a number or term stands alone it is referred to as being a monomial.
Answer (a) is correct

2.

113*x*^{7}

Monomial

Binomial

Trinomial

Polynomial

When a number or term stands alone it is referred to as being a monomial.
Answer (a) is correct

3.

30*x*^{2} + 17*x*^{2} - 4 + 12*x* - 3

Monomial

Binomial

Trinomial

Polynomial

When four or more monomial numbers or terms are linked together with either an addition sign, a minus sign or a multiplication sign, they are referred to as polynomials. Answer (d) is correct

4.

23*x*^{5} - 2*x*^{4} + 15*x*^{4}

Monomial

Binomial

Trinomial

Polynomial

When three monomial numbers or terms are linked together with either an addition sign, a minus sign or a multiplication sign, they are referred to as trinomials. Answer (c) is correct

5.

8*x*^{4} + 13 + 10*x*^{2}

Monomial

Binomial

Trinomial

Polynomial

6.

2*x*^{8} + 2*x*^{4} + 39 - 3*x*^{4}

Monomial

Binomial

Trinomial

Polynomial

7.

3*x*^{3} - 2*x*^{6}

Monomial

Binomial

Trinomial

Polynomial

When two monomial numbers or terms are linked together with either an addition sign, a minus sign or a multiplication sign, they are referred to as binomials. Answer (b) is correct

8.

55 + 17*x*^{2} + 9 - 5*x* + 21

Monomial

Binomial

Trinomial

Polynomial

9.

64

Monomial

Binomial

Trinomial

Polynomial

When a number or term stands alone it is referred to as being a monomial.
Answer (a) is correct

10.

99*x*^{2} + 51*x*^{2}

Monomial

Binomial

Trinomial

Polynomial

The next step is:

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