Which Polynomial Matches The Expression { -x(x-5)$}$?A. { X^2 - 5x$}$B. { X^2 + 5x$}$C. { -x^2 + 5x$}$D. { -2x - 5$}$

by ADMIN 118 views

Which Polynomial Matches the Expression −x(x−5){-x(x-5)}?

Understanding the Expression

The given expression is −x(x−5){-x(x-5)}. To determine which polynomial matches this expression, we need to expand and simplify it. The expression can be rewritten as −x2+5x{-x^2 + 5x} using the distributive property.

Analyzing the Options

Now, let's analyze the given options to find the one that matches the expression −x2+5x{-x^2 + 5x}.

Option A: x2−5x{x^2 - 5x}

This option does not match the expression −x2+5x{-x^2 + 5x} because the signs of the terms are different. In option A, the first term is positive, while in the expression, the first term is negative.

Option B: x2+5x{x^2 + 5x}

This option also does not match the expression −x2+5x{-x^2 + 5x} because the signs of the terms are different. In option B, the first term is positive, while in the expression, the first term is negative.

Option C: −x2+5x{-x^2 + 5x}

This option matches the expression −x2+5x{-x^2 + 5x} exactly. The signs and the terms are the same, making it the correct answer.

Option D: −2x−5{-2x - 5}

This option does not match the expression −x2+5x{-x^2 + 5x} because the terms are different. In option D, there is no term with a squared variable, and the constant term is negative, while in the expression, the constant term is not present.

Conclusion

Based on the analysis of the options, the correct answer is option C: −x2+5x{-x^2 + 5x}. This option matches the expression −x(x−5){-x(x-5)} exactly, making it the correct polynomial that matches the given expression.

Understanding the Concept

The concept of matching polynomials is an essential part of algebra. It requires the ability to expand and simplify expressions, as well as to analyze and compare different options. This concept is used in various mathematical applications, including solving equations and inequalities.

Real-World Applications

The concept of matching polynomials has real-world applications in various fields, including physics, engineering, and economics. For example, in physics, the motion of an object can be described using polynomial equations. In engineering, polynomial equations are used to model and analyze complex systems. In economics, polynomial equations are used to model and analyze economic systems.

Tips and Tricks

To solve problems involving matching polynomials, follow these tips and tricks:

  • Expand and simplify the expression using the distributive property.
  • Analyze and compare the options to find the one that matches the expression.
  • Use the correct signs and terms to match the expression.
  • Practice solving problems involving matching polynomials to develop your skills and confidence.

Common Mistakes

When solving problems involving matching polynomials, common mistakes include:

  • Failing to expand and simplify the expression.
  • Failing to analyze and compare the options.
  • Using the wrong signs or terms.
  • Not practicing enough to develop skills and confidence.

Conclusion

In conclusion, the correct answer is option C: −x2+5x{-x^2 + 5x}. This option matches the expression −x(x−5){-x(x-5)} exactly, making it the correct polynomial that matches the given expression. By understanding the concept of matching polynomials and following the tips and tricks, you can develop your skills and confidence in solving problems involving matching polynomials.
Q&A: Matching Polynomials

Frequently Asked Questions

Q: What is a polynomial?

A: A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication. Polynomials can be written in the form of anxn+an−1xn−1+…+a1x+a0{a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0}, where an{a_n}, an−1{a_{n-1}}, …{\ldots}, a1{a_1}, and a0{a_0} are coefficients, and x{x} is the variable.

Q: What is the distributive property?

A: The distributive property is a mathematical property that allows us to expand and simplify expressions by multiplying each term inside the parentheses by the term outside the parentheses. For example, a(b+c)=ab+ac{a(b + c) = ab + ac}.

Q: How do I expand and simplify a polynomial expression?

A: To expand and simplify a polynomial expression, follow these steps:

  1. Distribute the term outside the parentheses to each term inside the parentheses.
  2. Combine like terms by adding or subtracting the coefficients of the same variables.
  3. Simplify the expression by combining the terms.

Q: What is the difference between a polynomial and an expression?

A: A polynomial is a specific type of expression that consists of variables and coefficients combined using only addition, subtraction, and multiplication. An expression, on the other hand, can be any mathematical statement that includes variables, constants, and mathematical operations.

Q: How do I determine which polynomial matches a given expression?

A: To determine which polynomial matches a given expression, follow these steps:

  1. Expand and simplify the expression using the distributive property.
  2. Compare the expanded expression with the given options to find the one that matches.
  3. Use the correct signs and terms to match the expression.

Q: What are some common mistakes to avoid when solving problems involving matching polynomials?

A: Some common mistakes to avoid when solving problems involving matching polynomials include:

  • Failing to expand and simplify the expression.
  • Failing to analyze and compare the options.
  • Using the wrong signs or terms.
  • Not practicing enough to develop skills and confidence.

Q: How can I practice solving problems involving matching polynomials?

A: To practice solving problems involving matching polynomials, try the following:

  • Start with simple problems and gradually move on to more complex ones.
  • Practice expanding and simplifying polynomial expressions.
  • Analyze and compare different options to find the one that matches the expression.
  • Use online resources or math textbooks to find practice problems.

Q: What are some real-world applications of matching polynomials?

A: Some real-world applications of matching polynomials include:

  • Modeling and analyzing complex systems in physics, engineering, and economics.
  • Solving equations and inequalities in various fields.
  • Analyzing and comparing different options in decision-making.

Conclusion

In conclusion, matching polynomials is an essential concept in algebra that requires the ability to expand and simplify expressions, as well as to analyze and compare different options. By understanding the concept of matching polynomials and following the tips and tricks, you can develop your skills and confidence in solving problems involving matching polynomials.