https://r2.erweima.ai/mathbot/image/1725974156152wmdrnb3c.jpg

It seems that the image's text wasn't fully extracted properly. However, from visual observation, the quadratic equation to be factored is:

\[ 5x^2 + 7x + 2 \]

### To factor this quadratic expression:
1. Identify two numbers whose product is \(5 \times 2 = 10\) and whose sum is \(7\).
   - These two numbers are \(5\) and \(2\).

2. Rewrite the middle term \(7x\) using these two numbers:
   \[
   5x^2 + 5x + 2x + 2
   \]

3. Factor by grouping:
   \[
   5x(x + 1) + 2(x + 1)
   \]

4. Now, factor out the common binomial factor:
   \[
   (5x + 2)(x + 1)
   \]

Thus, the factored form of \(5x^2 + 7x + 2\) is:

\[
(5x + 2)(x + 1)
\]

Would you like any further clarification on the steps? 

Here are five related questions:
1. How do you factor quadratics when the leading coefficient is 1?
2. What are the conditions for a quadratic to be factorable over real numbers?
3. How do you check if your factorization is correct?
4. Can all quadratic equations be factored using integers?
5. How does factoring help in solving quadratic equations?

**Tip:** Always double-check by expanding your factors to ensure the correct result.

Factor the quadratic equation 5x^2 + 7x + 2

Learn how to factor the quadratic equation 5x^2 + 7x + 2 with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring by grouping. 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