Unit 5 Polynomial Functions Homework 2 Answer Key

Unit 5 of your mathematics course dives deep into polynomial functions. If you’re working on Homework 2 and looking for guidance, you’re in the right place. Understanding the intricacies of polynomial functions can be challenging, but with the right approach, you can master the concepts. Here, we’ll walk you through the answers and provide step-by-step solutions to help you grasp each part of the homework.

Understanding Polynomial Functions:
A polynomial function is a mathematical expression consisting of variables raised to different powers and combined using addition, subtraction, and multiplication. The general form of a polynomial is f(x)=anxn+an−1xn−1+⋯+a1x+a0f(x) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0f(x)=an​xn+an−1​xn−1+⋯+a1​x+a0​, where the exponents are non-negative integers, and the coefficients are constants.

Homework 2 Breakdown:
In this homework assignment, you’ll likely encounter problems that ask you to identify the degree of the polynomial, find its roots, and analyze its behavior. Let’s go through some key problems and solutions:

1. Problem 1: Find the degree of the polynomial f(x)=3×4−5×3+2×2−x+7f(x) = 3x^4 – 5x^3 + 2x^2 – x + 7f(x)=3×4−5×3+2×2−x+7.
   Solution: The degree of the polynomial is the highest exponent of xxx, which is 4. Hence, the degree is 4.
2. Problem 2: Solve 2×2−4x=02x^2 – 4x = 02×2−4x=0.
   Solution: Factor the polynomial to get 2x(x−2)=02x(x – 2) = 02x(x−2)=0, which gives roots at x=0x = 0x=0 and x=2x = 2x=2.
3. Problem 3: Find the sum of the roots of the polynomial f(x)=x3−6×2+11x−6f(x) = x^3 – 6x^2 + 11x – 6f(x)=x3−6×2+11x−6.
   Solution: By Vieta’s formulas, the sum of the roots is equal to the opposite of the coefficient of x2x^2×2, which is 6.

Common Mistakes to Avoid:
Many students make common errors when working with polynomial functions. A frequent mistake is overlooking the fact that polynomials can have complex roots or incorrectly factoring polynomials. Make sure to double-check your work to avoid such errors.

Tips for Success:

• Review the fundamental properties of polynomials, including their degrees and behaviors.
• Practice factoring and solving polynomial equations.
• Ensure that you understand the relationship between the coefficients and the roots.