https://file.aiquickdraw.com/mathbot/file/17267097313304yoeqf1n.jpg

The trinomial you are working with is:

\[
5x^2 + 39x + 28
\]

Let's factor this expression step by step.

### Step 1: Multiply the leading coefficient by the constant
The leading coefficient is \(5\) and the constant is \(28\). Multiply these together:

\[
5 \times 28 = 140
\]

### Step 2: Find two numbers that multiply to 140 and add to the middle term (39)
We need two numbers that multiply to 140 and add to 39. These numbers are \(35\) and \(4\), because:

\[
35 \times 4 = 140 \quad \text{and} \quad 35 + 4 = 39
\]

### Step 3: Rewrite the middle term using these two numbers
Now, rewrite \(39x\) as \(35x + 4x\):

\[
5x^2 + 35x + 4x + 28
\]

### Step 4: Factor by grouping
Group the terms into two pairs:

\[
(5x^2 + 35x) + (4x + 28)
\]

Now factor each group:

\[
5x(x + 7) + 4(x + 7)
\]

### Step 5: Factor out the common binomial
Since both terms have \((x + 7)\), factor it out:

\[
(5x + 4)(x + 7)
\]

### Final Factored Form:
The factored form of \(5x^2 + 39x + 28\) is:

\[
(5x + 4)(x + 7)
\]

Would you like more details on this process, or do you have any other questions?

---

Here are some related questions:
1. What are the steps to factor a trinomial with a leading coefficient other than 1?
2. How can factoring be used to solve quadratic equations?
3. What if the trinomial does not factor nicely — how do you use the quadratic formula?
4. Can you use factoring techniques for trinomials in higher-degree polynomials?
5. How does the distributive property help when factoring expressions?

**Tip:** Always double-check by multiplying the factored terms to ensure you get back the original expression.

Learn how to factor the trinomial 5x^2 + 39x + 28 with a detailed step-by-step guide. This problem uses the grouping method and applies core algebraic principles, including factorization and the distributive 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