Which expression is equivalent to x2−17x−60
?
A.(x−20)(x+3)

B.(x−5)(x−12)

C.(x−20)(x−3)

D.(x+5)(x−12)


To determine which expression is equivalent to \( x^2 - 17x - 60 \), let's factor the quadratic expression.

1. We start with \( x^2 - 17x - 60 \).
2. We need to find two numbers that multiply to \(-60\) and add up to \(-17\).
   - The numbers \(-20\) and \(3\) meet these criteria because:
     - \(-20 + 3 = -17\)
     - \(-20 \times 3 = -60\)

3. This allows us to factor the expression as:
   \[
   x^2 - 17x - 60 = (x - 20)(x + 3)
   \]

Therefore, the correct answer is:

**A. \( (x - 20)(x + 3) \)**

Would you like a deeper explanation or have any other questions?

---

Here are 5 related questions for additional practice:

1. What is the factored form of \( x^2 + 5x - 24 \)?
2. How do you determine the signs of the factors when factoring a quadratic with a negative constant term?
3. What is the factored form of \( x^2 - 13x + 36 \)?
4. Can \( x^2 + 17x + 60 \) be factored, and if so, what are the factors?
5. How would you factor \( x^2 - 9x + 20 \)?

**Tip:** When factoring, look for two numbers that add to the middle term and multiply to the constant term to simplify the process.

Which expression is equivalent to x^2−17x−60?
A.(x−20)(x+3)
B.(x−5)(x−12)
C.(x−20)(x−3)
D.(x+5)(x−12)

Explore how to factor the quadratic expression x^2 - 17x - 60 with a step-by-step solution. This problem covers fundamental algebra concepts, including identifying factors that meet specific criteria for middle and constant terms, using the Zero Product Property. Ideal for Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation