Evaluate The Given Expression For $x=4$.$x^3 - 4x^2 - 6x - 9$The Answer Is $\square \square$.

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Introduction

In this article, we will evaluate the given expression for x = 4. The expression is a cubic polynomial, and we will use algebraic techniques to simplify it and find its value.

The Expression

The given expression is:

x3−4x2−6x−9x^3 - 4x^2 - 6x - 9

We are asked to evaluate this expression for x = 4.

Substituting x = 4

To evaluate the expression, we will substitute x = 4 into the expression.

x3−4x2−6x−9x^3 - 4x^2 - 6x - 9

=(4)3−4(4)2−6(4)−9= (4)^3 - 4(4)^2 - 6(4) - 9

Simplifying the Expression

Now, we will simplify the expression by evaluating the powers of 4.

(4)3=64(4)^3 = 64

4(4)2=4(16)=644(4)^2 = 4(16) = 64

6(4)=246(4) = 24

So, the expression becomes:

=64−64−24−9= 64 - 64 - 24 - 9

Combining Like Terms

Now, we will combine like terms to simplify the expression further.

=64−64=0= 64 - 64 = 0

0−24=−240 - 24 = -24

−24−9=−33-24 - 9 = -33

So, the final value of the expression is:

=−33= -33

Conclusion

In this article, we evaluated the given expression for x = 4. We used algebraic techniques to simplify the expression and found its value to be -33.

Tips and Tricks

  • When evaluating expressions, always substitute the given value into the expression.
  • Use algebraic techniques to simplify the expression and combine like terms.
  • Check your work by plugging the final value back into the original expression.

Frequently Asked Questions

  • Q: What is the value of the expression for x = 4? A: The value of the expression for x = 4 is -33.
  • Q: How do I evaluate an expression for a given value? A: To evaluate an expression for a given value, substitute the value into the expression and use algebraic techniques to simplify it.

Related Topics

  • Evaluating expressions for given values
  • Algebraic techniques for simplifying expressions
  • Combining like terms

References

  • [1] Algebra textbook by [Author]
  • [2] Online resource for algebraic techniques

Keywords

  • Evaluate expression
  • Algebraic techniques
  • Simplifying expressions
  • Combining like terms
  • Cubic polynomial
  • Algebra

Introduction

Evaluating expressions is a fundamental concept in algebra that can be a bit tricky to grasp at first. However, with practice and patience, you can become proficient in evaluating expressions and solving problems with ease. In this article, we will provide a Q&A guide to help you understand the concept of evaluating expressions and how to apply it to real-world problems.

Q: What is an expression?

A: An expression is a combination of variables, constants, and mathematical operations that can be simplified to a single value.

Q: What is the difference between an expression and an equation?

A: An equation is a statement that says two expressions are equal, whereas an expression is a single value that can be calculated.

Q: How do I evaluate an expression?

A: To evaluate an expression, you need to substitute the given value into the expression and use algebraic techniques to simplify it.

Q: What are some common algebraic techniques used to simplify expressions?

A: Some common algebraic techniques used to simplify expressions include:

  • Combining like terms
  • Distributing coefficients
  • Using the order of operations (PEMDAS)

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a mnemonic device that helps you remember the order in which to perform mathematical operations:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I combine like terms?

A: To combine like terms, you need to identify the terms that have the same variable and coefficient, and then add or subtract them.

Q: What is the difference between a variable and a constant?

A: A variable is a letter or symbol that represents a value that can change, whereas a constant is a value that remains the same.

Q: How do I distribute coefficients?

A: To distribute coefficients, you need to multiply each term in the expression by the coefficient.

Q: What is the importance of evaluating expressions?

A: Evaluating expressions is an essential skill in algebra that helps you solve problems and make informed decisions.

Q: How can I practice evaluating expressions?

A: You can practice evaluating expressions by working through algebraic problems and exercises, and by using online resources and tools to help you learn.

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

A: Some common mistakes to avoid when evaluating expressions include:

  • Forgetting to distribute coefficients
  • Not following the order of operations (PEMDAS)
  • Not combining like terms
  • Not checking your work

Q: How can I improve my skills in evaluating expressions?

A: You can improve your skills in evaluating expressions by:

  • Practicing regularly
  • Seeking help from a teacher or tutor
  • Using online resources and tools
  • Reviewing and practicing algebraic techniques

Q: What are some real-world applications of evaluating expressions?

A: Evaluating expressions has many real-world applications, including:

  • Calculating costs and revenues in business
  • Determining the area and perimeter of shapes in geometry
  • Modeling population growth and decay in biology
  • Solving problems in physics and engineering

Q: How can I apply evaluating expressions to real-world problems?

A: You can apply evaluating expressions to real-world problems by:

  • Identifying the variables and constants in the problem
  • Using algebraic techniques to simplify the expression
  • Evaluating the expression using the given values
  • Interpreting the results and making informed decisions

Conclusion

Evaluating expressions is a fundamental concept in algebra that can be applied to a wide range of real-world problems. By understanding the basics of evaluating expressions and practicing regularly, you can become proficient in solving problems and making informed decisions. Remember to always follow the order of operations (PEMDAS), combine like terms, and check your work to ensure accuracy.

Tips and Tricks

  • Practice regularly to improve your skills in evaluating expressions.
  • Use online resources and tools to help you learn and practice.
  • Review and practice algebraic techniques to ensure accuracy.
  • Seek help from a teacher or tutor if you need additional support.

Frequently Asked Questions

  • Q: What is an expression? A: An expression is a combination of variables, constants, and mathematical operations that can be simplified to a single value.
  • Q: How do I evaluate an expression? A: To evaluate an expression, you need to substitute the given value into the expression and use algebraic techniques to simplify it.

Related Topics

  • Algebraic techniques for simplifying expressions
  • Combining like terms
  • Distributing coefficients
  • Order of operations (PEMDAS)

References

  • [1] Algebra textbook by [Author]
  • [2] Online resource for algebraic techniques
  • [3] Real-world applications of evaluating expressions

Keywords

  • Evaluate expression
  • Algebraic techniques
  • Simplifying expressions
  • Combining like terms
  • Distributing coefficients
  • Order of operations (PEMDAS)
  • Algebra