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To solve the problem of finding an expression equivalent to \( -28x^2 + 35x \), we need to factor out the greatest common factor (GCF) from the terms. 

1. Identify the GCF of \(-28x^2\) and \(35x\):
   - The coefficients are \(-28\) and \(35\).
   - The GCF of \(-28\) and \(35\) is \(7\).
   - Both terms contain the variable \(x\).

2. Factor out the GCF \(7x\) from each term:
   \[
   -28x^2 + 35x = 7x \left(\frac{-28x^2}{7x} + \frac{35x}{7x}\right)
   \]
   Simplifying inside the parentheses:
   \[
   7x \left(-4x + 5\right)
   \]

3. Thus, the factored form of \( -28x^2 + 35x \) is:
   \[
   7x(-4x + 5)
   \]

Since the question asks for the expression equivalent to \( -28x^2 + 35x \), the correct answer from the given choices is:
\[
-7x(4x - 5)
\]

Would you like further details or have any questions about this solution?

Here are some related questions to expand your understanding:

1. How do you determine the greatest common factor of two numbers?
2. What is the process for factoring a polynomial?
3. How can you check if a factored expression is equivalent to the original expression?
4. Why is it important to factor out the greatest common factor first in polynomial factorization?
5. Can the method used to factor \(-28x^2 + 35x\) be applied to other polynomials? If so, how?

**Tip:** When factoring polynomials, always start by factoring out the greatest common factor from all terms. This simplifies the expression and makes further factoring easier.

Which expression is equivalent to -28x^2 + 35x?

Learn how to factor the algebraic expression -28x^2 + 35x by finding the greatest common factor (GCF). This problem involves factoring out the GCF from a quadratic term and linear term. Suitable for students in Grades 8-10.

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