Lesson 1: Polynomials CE 2015
Algebra Readiness (Pre-Algebra) B Unit 4: Polynomials and Properties of Exponents plz help
Of course, I'm here to help! Polynomials and properties of exponents can seem overwhelming at first, but with a little explanation, you'll be able to understand and solve problems related to this topic.
To start, let's review what polynomials are. A polynomial is an algebraic expression that consists of variables, coefficients, and exponents. It can have multiple terms, which are separated by addition or subtraction operators.
For example, here are some examples of polynomials:
1. 3x^2 + 4x - 1
2. 2a^3 - 5a^2 + a
3. 7xy^2 - 2y + 1
Now, let's move on to the properties of exponents. Exponents are used to represent repeated multiplication of a number or variable. There are several properties of exponents that can help us simplify and solve polynomial expressions. Here are some key properties:
1. Product of Powers: When multiplying two terms with the same base, you add their exponents. For example, x^m * x^n = x^(m+n).
2. Quotient of Powers: When dividing two terms with the same base, you subtract the exponent of the denominator from the exponent of the numerator. For example, x^m / x^n = x^(m-n).
3. Power of a Power: When raising a power to another exponent, you multiply the exponents. For example, (x^m)^n = x^(m*n).
4. Power of a Product: When raising a product to an exponent, you distribute the exponent to each term inside the parentheses. For example, (xy)^n = x^n * y^n.
Now, let's go over a practice problem to apply these concepts:
Problem: Simplify the expression (2x^2 y^3)^4 / (xy)^2.
Solution:
Step 1: Apply the Power of a Power rule.
(2x^2 y^3)^4 = 2^4 * (x^2)^4 * (y^3)^4 = 16x^8 * y^12
Step 2: Apply the Power of a Product rule.
(xy)^2 = x^2 * y^2
Step 3: Apply the Quotient of Powers rule.
(16x^8 * y^12) / (x^2 * y^2) = 16 * (x^8 / x^2) * (y^12 / y^2) = 16x^(8-2) * y^(12-2) = 16x^6 * y^10
So, the simplified expression is 16x^6 * y^10.
I hope this explanation helps you understand polynomials and properties of exponents better. If you have any more specific questions or need further assistance, please let me know!