UNIT 4
Polynomials and Properties of Exponents
LESSON 7
Polynomials and Properties of Exponents Unit Test
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In this unit, you have learned about polynomials and the properties of exponents. Here is a brief overview of these topics:
1. Polynomials: A polynomial is a mathematical expression that consists of variables, coefficients, and non-negative integer exponents. It can be a constant, a single term, or multiple terms added or subtracted together. For example, 2x^2 + 3x - 1 is a polynomial with three terms.
2. Degree of a Polynomial: The degree of a polynomial is the highest exponent of its terms. It provides information about the complexity or size of the polynomial. The degree of a term is the sum of the exponents of the variables in that term. For example, the polynomial 2x^3 + 3x^2 - 5x + 1 is of degree 3 because the highest exponent is 3.
3. Addition, Subtraction, Multiplication of Polynomials: To add or subtract polynomials, you combine like terms. Like terms have the same variables raised to the same exponents. To multiply polynomials, you can use the distributive property or the FOIL method.
4. Properties of Exponents: Exponents represent repeated multiplication. Here are some properties of exponents:
a. Product Rule: a^m * a^n = a^(m+n)
b. Quotient Rule: a^m / a^n = a^(m-n)
c. Power Rule: (a^m)^n = a^(m*n)
d. Zero Exponent Rule: a^0 = 1
e. Negative Exponent Rule: a^(-m) = 1 / a^m
To successfully answer questions related to polynomials and the properties of exponents, make sure to review the concepts mentioned above and practice solving different types of problems.