### About What is a Polynomial:

A polynomial is the most basic type of algebraic expression that one can encounter. A polynomial can be a single term or the sum of a finite number of terms where each variable has only non-negative integer exponents. With polynomials, we have the monomial, binomial, and trinomial that occur very frequently. Additionally, we write our polynomial in standard form by arranging the polynomial in descending order of powers. When a polynomial has a single variable, this means the term with the variable that has the highest power is listed at the furthest left and is followed by the next highest power. This pattern continues until all terms of the polynomial have been listed.

Test Objectives

- Demonstrate the ability to determine if two or more terms are "like terms"
- Demonstrate an understanding of the definition of a polynomial
- Demonstrate an understanding of how to determine the degree of a term
- Demonstrate an understanding of how to determine the degree of a polynomial
- Demonstrate an understanding of how to write a polynomial in standard form

#1:

Instructions: Determine if each pair of terms are "like terms".

$$a)\hspace{.2em}3x, 7xy$$

$$b)\hspace{.2em}2x^2y, -9yx^2$$

$$c)\hspace{.2em}-14x^4y^2z, 7x^2y^4z$$

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#2:

Instructions: Determine if the following algebraic expression represents a polynomial.

$$a)\hspace{.2em}\frac{1}{3}x^2 - \frac{3}{5}x + 3$$

$$b)\hspace{.2em}9x^3 - \sqrt{x}+ 13$$

$$c)\hspace{.2em}\frac{2}{3}x^2 - x + \frac{5}{x}$$

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#3:

Instructions: Write each polynomial in standard form.

$$a)\hspace{.2em}9x^3 - 7x^4 + 4x^2 - x + 8$$

$$b)\hspace{.2em}12xy - 4x^2y - x + 5x^3y^2 - 1$$

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#4:

Instructions: Find the degree of each polynomial.

$$a)\hspace{.2em}19x^5y^2 - 12x^8y + 13xy - 5$$

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#5:

Instructions: Find the degree of each polynomial.

$$a)\hspace{.2em}20x^2y^2z^2 - 15x^9 + 7y^5z^3$$

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Written Solutions:

#1:

Solutions:

a) Not Like Terms

b) Like Terms

c) Not Like Terms

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#2:

Solutions:

a) Polynomial

b) Not a Polynomial

c) Not a Polynomial

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#3:

Solutions:

$$a)\hspace{.2em}-7x^4 + 9x^3 + 4x^2 - x + 8$$

$$b)\hspace{.2em}5x^3y^2 - 4x^2y + 12xy - x - 1$$

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#4:

Solutions:

a) Degree: 9

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#5:

Solutions:

a) Degree: 9