Evaluate The Expression For X = − 2 X = -2 X = − 2 . 4 X 3 − 3 X 2 + 2 4x^3 - 3x^2 + 2 4 X 3 − 3 X 2 + 2

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Introduction

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In algebra, evaluating an expression involves substituting a given value for a variable and simplifying the resulting expression. In this article, we will evaluate the expression $4x^3 - 3x^2 + 2$ for $x = -2$. This will involve substituting $x = -2$ into the expression and simplifying the resulting expression.

Understanding the Expression

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The given expression is a polynomial expression of degree 3, which means it has three terms with different powers of $x$. The expression is $4x^3 - 3x^2 + 2$, where $x$ is the variable. To evaluate this expression, we need to substitute $x = -2$ into the expression and simplify the resulting expression.

Substituting $x = -2$ into the Expression

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To substitute $x = -2$ into the expression, we need to replace every occurrence of $x$ with $-2$. This will give us the expression $4(-2)^3 - 3(-2)^2 + 2$.

Evaluating the Expression

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To evaluate the expression $4(-2)^3 - 3(-2)^2 + 2$, we need to follow the order of operations (PEMDAS):

1. Evaluate the exponents: $(-2)^3 = -8$ and $(-2)^2 = 4$
2. Multiply the coefficients by the results of the exponents: $4(-8) = -32$ and $3(4) = 12$
3. Add and subtract the results: $-32 - 12 + 2 = -42$

Conclusion

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In this article, we evaluated the expression $4x^3 - 3x^2 + 2$ for $x = -2$. We substituted $x = -2$ into the expression and simplified the resulting expression to get the final answer of $-42$.

Example Use Cases

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Evaluating expressions is a fundamental concept in algebra and is used in a wide range of applications, including:

• Science and Engineering: Evaluating expressions is used to model real-world phenomena and make predictions about the behavior of physical systems.
• Computer Programming: Evaluating expressions is used in programming languages to perform calculations and make decisions.
• Finance: Evaluating expressions is used to calculate financial metrics, such as interest rates and investment returns.

Tips and Tricks

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When evaluating expressions, it's essential to follow the order of operations (PEMDAS) to ensure that the expression is evaluated correctly. Additionally, it's crucial to substitute the given value for the variable correctly and simplify the resulting expression.

Common Mistakes

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When evaluating expressions, some common mistakes to avoid include:

• Not following the order of operations: Failing to follow the order of operations (PEMDAS) can lead to incorrect results.
• Not substituting the given value correctly: Failing to substitute the given value for the variable correctly can lead to incorrect results.
• Not simplifying the resulting expression: Failing to simplify the resulting expression can lead to incorrect results.

Final Thoughts

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Evaluating expressions is a fundamental concept in algebra that is used in a wide range of applications. By following the order of operations (PEMDAS) and substituting the given value correctly, we can ensure that the expression is evaluated correctly and simplify the resulting expression to get the final answer.

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Introduction

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In our previous article, we evaluated the expression $4x^3 - 3x^2 + 2$ for $x = -2$. In this article, we will provide a Q&A guide to help you understand the concept of evaluating expressions and how to apply it in different situations.

Q&A

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Q: What is an expression in algebra?

A: An expression in algebra is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division.

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

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when evaluating an expression. The acronym PEMDAS stands for:

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

Q: How do I evaluate an expression with exponents?

A: To evaluate an expression with exponents, you need to follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. For example, to evaluate the expression $2^3$, you would first evaluate the exponent $3$, which is equal to $3$. Then, you would multiply $2$ by the result, which is equal to $8$.

Q: How do I evaluate an expression with multiple variables?

A: To evaluate an expression with multiple variables, you need to substitute the given values for each variable into the expression. For example, to evaluate the expression $x^2 + 2y$, you would first substitute the given value for $x$ into the expression. Then, you would substitute the given value for $y$ into the expression.

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

A: An expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division. An equation is a statement that says two expressions are equal, such as $x + 2 = 5$.

Q: How do I simplify an expression?

A: To simplify an expression, you need to combine like terms and eliminate any unnecessary operations. For example, to simplify the expression $2x + 3x$, you would combine the like terms $2x$ and $3x$ to get $5x$.

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

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

• Not following the order of operations: Failing to follow the order of operations (PEMDAS) can lead to incorrect results.
• Not substituting the given value correctly: Failing to substitute the given value for the variable correctly can lead to incorrect results.
• Not simplifying the resulting expression: Failing to simplify the resulting expression can lead to incorrect results.

Example Problems

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Problem 1: Evaluate the expression $2x^2 + 3x - 1$ for $x = 2$.

Solution: To evaluate the expression $2x^2 + 3x - 1$ for $x = 2$, we need to substitute $x = 2$ into the expression and simplify the resulting expression.

$2(2)^2 + 3(2) - 1$ $= 2(4) + 6 - 1$ $= 8 + 6 - 1$ $= 13$

Problem 2: Evaluate the expression $x^3 - 2x^2 + 3x$ for $x = -1$.

Solution: To evaluate the expression $x^3 - 2x^2 + 3x$ for $x = -1$, we need to substitute $x = -1$ into the expression and simplify the resulting expression.

$(-1)^3 - 2(-1)^2 + 3(-1)$ $= -1 - 2(-1) - 3$ $= -1 + 2 - 3$ $= -2$

Conclusion

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Evaluating expressions is a fundamental concept in algebra that is used in a wide range of applications. By following the order of operations (PEMDAS) and substituting the given value correctly, we can ensure that the expression is evaluated correctly and simplify the resulting expression to get the final answer.