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The given problem asks for an expression that is equivalent to \( x^2 - 17x - 60 \).

We can solve this by factoring the quadratic expression \( x^2 - 17x - 60 \).

### Step 1: Find two numbers that multiply to \(-60\) and add to \(-17\).
We need to find two numbers that satisfy these conditions:
- Product = \(-60\)
- Sum = \(-17\)

The numbers \(-20\) and \(3\) work because:
- \(-20 \times 3 = -60\)
- \(-20 + 3 = -17\)

### Step 2: Write the factored form.
Using these numbers, we can factor the quadratic expression as:
\[
x^2 - 17x - 60 = (x - 20)(x + 3)
\]

Thus, the correct answer is:
\[
(x - 20)(x + 3)
\]

However, in the provided image, the user selected option C: \((x - 20)(x - 3)\). This is incorrect because the second factor should be \((x + 3)\), not \((x - 3)\). The correct answer would actually be option A, \((x - 20)(x + 3)\).

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

Here are 5 related questions to consider:
1. How do you factor more complex quadratic expressions?
2. Can all quadratic equations be factored like this?
3. What is the general process for factoring trinomials?
4. How would the solution change if the sign of the constant term were different?
5. What is the relationship between the factored form and the roots of the quadratic equation?

**Tip**: Always verify your factors by expanding them back to ensure they match the original quadratic expression.

Which expression is equivalent to x^2 - 17x - 60?

Learn how to factor the quadratic equation x^2 - 17x - 60 by finding two numbers that multiply to -60 and add to -17. Detailed step-by-step solution provided for students in Grades 8-10.

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