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