https://file.aiquickdraw.com/mathbot/file/1726082743721lq72azul.jpg

The trinomial in the image is:

\[
5x^2 + 36x + 7
\]

To factor this trinomial, we use the method of splitting the middle term (since the coefficient of \(x^2\) is greater than 1).

### Step 1: Multiply the leading coefficient and the constant term
\[
5 \times 7 = 35
\]

### Step 2: Find two numbers that multiply to 35 and add to 36
The two numbers are 35 and 1, because:
\[
35 \times 1 = 35 \quad \text{and} \quad 35 + 1 = 36
\]

### Step 3: Split the middle term
Rewrite the trinomial by splitting the middle term:
\[
5x^2 + 35x + 1x + 7
\]

### Step 4: Factor by grouping
Group the terms into two pairs:
\[
(5x^2 + 35x) + (1x + 7)
\]

Factor each group:
\[
5x(x + 7) + 1(x + 7)
\]

### Step 5: Factor out the common binomial
\[
(5x + 1)(x + 7)
\]

Thus, the factored form of the trinomial is:
\[
(5x + 1)(x + 7)
\]

Would you like more details or have any questions about this process?

Here are 5 related questions:
1. How do you factor trinomials when \(a = 1\)?
2. What is the "AC" method of factoring trinomials?
3. Can all trinomials be factored?
4. What happens if no pair of factors of the product equals the middle term's coefficient?
5. How does factoring help solve quadratic equations?

**Tip:** Always check your factorization by expanding the factored form to see if it equals the original trinomial.

Learn how to factor the trinomial 5x^2 + 36x + 7 by splitting the middle term and factoring by grouping. This problem covers key algebra concepts suitable for Grades 8-10.

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