Given The Polynomial Function Below, Find $F(-5$\].$F(x) = X^2 - 2x - 7$A. 28 B. -22 C. 8 D. -42

Introduction

Polynomial functions are a fundamental concept in algebra, and evaluating them is a crucial skill for students to master. In this article, we will explore how to evaluate a polynomial function at a given value, using the function $F(x) = x^2 - 2x - 7$ as an example. We will also provide a step-by-step guide on how to evaluate the function at $x = -5$.

What is a Polynomial Function?

A polynomial function is a function that can be written in the form $f(x) = a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$, where $a_n, a_{n-1}, \ldots, a_1, a_0$ are constants, and $n$ is a non-negative integer. The degree of the polynomial is the highest power of $x$ in the function.

Evaluating a Polynomial Function

To evaluate a polynomial function at a given value, we simply substitute the value into the function and simplify. Let's use the function $F(x) = x^2 - 2x - 7$ as an example.

Step 1: Substitute the Value into the Function

We want to evaluate the function at $x = -5$. To do this, we substitute $x = -5$ into the function:

$F(-5) = (-5)^2 - 2(-5) - 7$

Step 2: Simplify the Expression

Now, we simplify the expression by evaluating the exponent and multiplying:

$F(-5) = 25 + 10 - 7$

Step 3: Combine Like Terms

Next, we combine the like terms:

$F(-5) = 28$

Conclusion

In this article, we evaluated the polynomial function $F(x) = x^2 - 2x - 7$ at $x = -5$. We followed a step-by-step guide to substitute the value into the function, simplify the expression, and combine like terms. The final answer is $F(-5) = 28$.

Example Problems

Here are a few example problems to practice evaluating polynomial functions:

1. Evaluate the function $F(x) = x^2 + 3x - 2$ at $x = 2$.
2. Evaluate the function $F(x) = 2x^2 - 5x + 1$ at $x = -1$.
3. Evaluate the function $F(x) = x^3 - 4x^2 + 3x + 1$ at $x = 2$.

Tips and Tricks

Here are a few tips and tricks to help you evaluate polynomial functions:

• Make sure to substitute the value into the function correctly.
• Simplify the expression by evaluating the exponent and multiplying.
• Combine like terms to get the final answer.

Common Mistakes

Here are a few common mistakes to avoid when evaluating polynomial functions:

• Not substituting the value into the function correctly.
• Not simplifying the expression correctly.
• Not combining like terms correctly.

Conclusion

Introduction

In our previous article, we explored how to evaluate a polynomial function at a given value, using the function $F(x) = x^2 - 2x - 7$ as an example. In this article, we will provide a Q&A guide to help you understand the concept of evaluating polynomial functions better.

Q: What is a polynomial function?

A: A polynomial function is a function that can be written in the form $f(x) = a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$, where $a_n, a_{n-1}, \ldots, a_1, a_0$ are constants, and $n$ is a non-negative integer.

Q: How do I evaluate a polynomial function at a given value?

A: To evaluate a polynomial function at a given value, you simply substitute the value into the function and simplify. Let's use the function $F(x) = x^2 - 2x - 7$ as an example.

Q: What is the first step in evaluating a polynomial function?

A: The first step in evaluating a polynomial function is to substitute the value into the function.

Q: How do I simplify the expression after substituting the value?

A: After substituting the value into the function, you simplify the expression by evaluating the exponent and multiplying.

Q: What is the next step after simplifying the expression?

A: The next step is to combine like terms to get the final answer.

Q: What are some common mistakes to avoid when evaluating polynomial functions?

A: Some common mistakes to avoid when evaluating polynomial functions include:

• Not substituting the value into the function correctly.
• Not simplifying the expression correctly.
• Not combining like terms correctly.

Q: How can I practice evaluating polynomial functions?

A: You can practice evaluating polynomial functions by using example problems and following a step-by-step guide.

Q: What are some tips and tricks to help me evaluate polynomial functions?

A: Some tips and tricks to help you evaluate polynomial functions include:

• Make sure to substitute the value into the function correctly.
• Simplify the expression by evaluating the exponent and multiplying.
• Combine like terms to get the final answer.

Q: Can I use a calculator to evaluate polynomial functions?

A: Yes, you can use a calculator to evaluate polynomial functions. However, it's always a good idea to follow a step-by-step guide and understand the concept behind the calculation.

Q: How can I apply the concept of evaluating polynomial functions to real-world problems?

A: The concept of evaluating polynomial functions can be applied to real-world problems such as:

• Modeling population growth
• Analyzing financial data
• Predicting weather patterns

Conclusion

Evaluating polynomial functions is a crucial skill for students to master. By following a step-by-step guide and practicing example problems, you can become proficient in evaluating polynomial functions. Remember to substitute the value into the function correctly, simplify the expression, and combine like terms to get the final answer.

Example Problems

Here are a few example problems to practice evaluating polynomial functions:

1. Evaluate the function $F(x) = x^2 + 3x - 2$ at $x = 2$.
2. Evaluate the function $F(x) = 2x^2 - 5x + 1$ at $x = -1$.
3. Evaluate the function $F(x) = x^3 - 4x^2 + 3x + 1$ at $x = 2$.

Answer Key

Here are the answers to the example problems:

1. $F(2) = 2^2 + 3(2) - 2 = 4 + 6 - 2 = 8$
2. $F(-1) = 2(-1)^2 - 5(-1) + 1 = 2 + 5 + 1 = 8$
3. $F(2) = 2^3 - 4(2)^2 + 3(2) + 1 = 8 - 16 + 6 + 1 = -1$

Conclusion

Evaluating polynomial functions is a crucial skill for students to master. By following a step-by-step guide and practicing example problems, you can become proficient in evaluating polynomial functions. Remember to substitute the value into the function correctly, simplify the expression, and combine like terms to get the final answer.