To factor the quadratic polynomial \( x^2 - 15x + 50 \), follow these steps:

1. We need to find two numbers that multiply to give the constant term (50) and add up to the coefficient of the linear term (-15).

2. The pair of numbers that satisfy these conditions are -5 and -10 because:
   - \( -5 \times -10 = 50 \)
   - \( -5 + (-10) = -15 \)

3. Now, express the quadratic in its factored form:
   \[
   x^2 - 15x + 50 = (x - 5)(x - 10)
   \]

So, the factored form of \( x^2 - 15x + 50 \) is:
\[
(x - 5)(x - 10)
\]

Would you like more details or further clarification on any step?

Here are 5 related questions you can try:
1. Factor \( x^2 - 10x + 24 \).
2. Solve \( (x - 5)(x - 10) = 0 \).
3. Expand \( (x - 3)(x - 7) \) and compare the process.
4. Find the roots of \( x^2 - 15x + 50 \).
5. What happens to the factored form if we add 10 to the constant term?

**Tip:** Always check your factored form by expanding it back to ensure it matches the original expression.

Learn how to factor the quadratic polynomial x^2 - 15x + 50 with a step-by-step explanation. Discover the key algebraic concepts, such as factoring and the zero product property, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation