Evaluate $5x^2 + 2x - 15$ For $x = -2$.A. 31 B. 26 C. 1 D. -31

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Introduction

In algebra, evaluating an expression means finding its value when the variable is replaced by a specific number. In this article, we will learn how to evaluate the quadratic expression $5x^2 + 2x - 15$ when $x = -2$. This involves substituting the value of $x$ into the expression and simplifying the resulting expression.

Understanding the Expression

The given expression is a quadratic expression in the form of $ax^2 + bx + c$, where $a = 5$, $b = 2$, and $c = -15$. To evaluate this expression for $x = -2$, we need to substitute $x = -2$ into the expression and simplify.

Substituting $x = -2$ into the Expression

To substitute $x = -2$ into the expression, we replace every occurrence of $x$ with $-2$. This gives us:

$$5(-2)^2 + 2(-2) - 15$$

Simplifying the Expression

Now, we need to simplify the expression by evaluating the exponents and multiplying the coefficients.

$$5(-2)^2 + 2(-2) - 15$$

$$= 5(4) + 2(-2) - 15$$

$$= 20 + 2(-2) - 15$$

$$= 20 - 4 - 15$$

$$= 16 - 15$$

$$= 1$$

Conclusion

Therefore, the value of the expression $5x^2 + 2x - 15$ when $x = -2$ is $1$.

Final Answer

The final answer is $\boxed{1}$.

Discussion

The expression $5x^2 + 2x - 15$ is a quadratic expression that can be evaluated for any value of $x$. In this article, we evaluated the expression for $x = -2$ and found that the value of the expression is $1$. This demonstrates the importance of evaluating expressions in algebra, as it allows us to find the value of an expression for a specific value of the variable.

Common Mistakes

When evaluating expressions, it's easy to make mistakes. Some common mistakes include:

• Not substituting the value of the variable into the expression
• Not simplifying the expression correctly
• Not following the order of operations (PEMDAS)

To avoid these mistakes, it's essential to carefully read the problem and follow the steps to evaluate the expression.

Tips and Tricks

Here are some tips and tricks to help you evaluate expressions:

• Always read the problem carefully and understand what is being asked
• Substitute the value of the variable into the expression
• Simplify the expression by following the order of operations (PEMDAS)
• Check your work by plugging the value of the expression back into the original equation

By following these tips and tricks, you can become proficient in evaluating expressions and solving algebraic problems.

Real-World Applications

Evaluating expressions has many real-world applications. For example:

• In physics, evaluating expressions is used to calculate the trajectory of an object under the influence of gravity.
• In engineering, evaluating expressions is used to design and optimize systems.
• In finance, evaluating expressions is used to calculate the value of investments.

In conclusion, evaluating expressions is a fundamental concept in algebra that has many real-world applications. By following the steps outlined in this article, you can become proficient in evaluating expressions and solving algebraic problems.

Frequently Asked Questions

Q: What is the value of the expression $5x^2 + 2x - 15$ when $x = -2$? A: The value of the expression $5x^2 + 2x - 15$ when $x = -2$ is $1$.

Q: How do I evaluate an expression? A: To evaluate an expression, substitute the value of the variable into the expression and simplify by following the order of operations (PEMDAS).

Q: What are some common mistakes to avoid when evaluating expressions? A: Some common mistakes to avoid when evaluating expressions include not substituting the value of the variable into the expression, not simplifying the expression correctly, and not following the order of operations (PEMDAS).

Q: What are some real-world applications of evaluating expressions? A: Evaluating expressions has many real-world applications, including physics, engineering, and finance.

References

• [1] Algebra for Dummies, by Mary Jane Sterling
• [2] Calculus for Dummies, by Mark Ryan
• [3] Mathematics for Dummies, by Mary Jane Sterling

Note: The references provided are for general information purposes only and are not specific to the topic of evaluating expressions.

Introduction

Evaluating expressions is a fundamental concept in algebra that has many real-world applications. In this article, we will provide a comprehensive Q&A guide to help you understand how to evaluate expressions and solve algebraic problems.

Q&A

Q: What is the value of the expression $5x^2 + 2x - 15$ when $x = -2$?

A: The value of the expression $5x^2 + 2x - 15$ when $x = -2$ is $1$.

Q: How do I evaluate an expression?

A: To evaluate an expression, substitute the value of the variable into the expression and simplify by following the order of operations (PEMDAS).

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

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

• Not substituting the value of the variable into the expression
• Not simplifying the expression correctly
• Not following the order of operations (PEMDAS)

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

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

• P: Parentheses
• E: Exponents
• M: Multiplication
• D: Division
• A: Addition
• S: Subtraction

Q: How do I simplify an expression?

A: To simplify an expression, follow the order of operations (PEMDAS) and combine like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable and exponent. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ and the exponent $1$.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the like terms. For example, $2x + 5x = 7x$.

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

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

• Physics: Evaluating expressions is used to calculate the trajectory of an object under the influence of gravity.
• Engineering: Evaluating expressions is used to design and optimize systems.
• Finance: Evaluating expressions is used to calculate the value of investments.

Q: How do I evaluate an expression with fractions?

A: To evaluate an expression with fractions, follow the same steps as evaluating an expression with integers. However, be sure to simplify the fractions by dividing the numerator and denominator by their greatest common divisor.

Q: How do I evaluate an expression with decimals?

A: To evaluate an expression with decimals, follow the same steps as evaluating an expression with integers. However, be sure to round the answer to the correct number of decimal places.

Q: What are some tips and tricks for evaluating expressions?

A: Some tips and tricks for evaluating expressions include:

• Always read the problem carefully and understand what is being asked
• Substitute the value of the variable into the expression
• Simplify the expression by following the order of operations (PEMDAS)
• Check your work by plugging the value of the expression back into the original equation

Conclusion

Evaluating expressions is a fundamental concept in algebra that has many real-world applications. By following the steps outlined in this article, you can become proficient in evaluating expressions and solving algebraic problems.

Frequently Asked Questions

Q: What is the value of the expression $5x^2 + 2x - 15$ when $x = -2$? A: The value of the expression $5x^2 + 2x - 15$ when $x = -2$ is $1$.

Q: How do I evaluate an expression? A: To evaluate an expression, substitute the value of the variable into the expression and simplify by following the order of operations (PEMDAS).

Q: What are some common mistakes to avoid when evaluating expressions? A: Some common mistakes to avoid when evaluating expressions include not substituting the value of the variable into the expression, not simplifying the expression correctly, and not following the order of operations (PEMDAS).

Q: What are some real-world applications of evaluating expressions? A: Evaluating expressions has many real-world applications, including physics, engineering, and finance.

References

• [1] Algebra for Dummies, by Mary Jane Sterling
• [2] Calculus for Dummies, by Mark Ryan
• [3] Mathematics for Dummies, by Mary Jane Sterling

Note: The references provided are for general information purposes only and are not specific to the topic of evaluating expressions.