https://file.aiquickdraw.com/mathbot/file/1729997560240uh3o5773.jpg

The problem in the image asks to factor the polynomial:

\[
(x - 11)^2 + 10(x - 11) - 200
\]

Let's solve this step-by-step:

1. **Substitute** \( u = x - 11 \), which makes the polynomial easier to handle. So, the expression becomes:
   \[
   u^2 + 10u - 200
   \]

2. **Factor** \( u^2 + 10u - 200 \):
   We need two numbers that multiply to \(-200\) and add up to \(10\). These numbers are \(20\) and \(-10\).

   Therefore,
   \[
   u^2 + 10u - 200 = (u + 20)(u - 10)
   \]

3. **Replace \( u \) back with \( x - 11 \)**:
   \[
   (x - 11 + 20)(x - 11 - 10) = (x + 9)(x - 21)
   \]

So, the complete factorization is:

\[
(x + 9)(x - 21)
\]

The correct answer is:

**A.** \((x - 11)^2 + 10(x - 11) - 200 = (x + 9)(x - 21)\)

Would you like more details on any part of the solution?

---

Here are some related questions:

1. What are common methods for factoring quadratic polynomials?
2. How can substitution simplify factoring complex expressions?
3. Why is it necessary to test possible factors in factoring problems?
4. What are the steps to revert substitution in polynomial factoring?
5. How does completing the square compare with other factoring techniques?

**Tip:** Always look for patterns or substitutions to simplify polynomial expressions before factoring.

Learn how to factor the polynomial (x - 11)^2 + 10(x - 11) - 200 with a step-by-step solution. This solution demonstrates polynomial factorization using substitution, ideal for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation