https://file.aiquickdraw.com/mathbot/file/1726082795398eos7ku9u.jpg

The expression given in the image is \( 5x^2 + 26x + 24 \), and you're asked to factor it.

Let's go through the factoring process step by step:

### Step 1: Multiply the coefficient of \(x^2\) by the constant term.
Here, the coefficient of \(x^2\) is 5, and the constant term is 24.

So, \( 5 \times 24 = 120 \).

### Step 2: Find two numbers that multiply to 120 and add up to the middle term's coefficient (26).
The two numbers are 10 and 12, because:
\[ 10 \times 12 = 120 \quad \text{and} \quad 10 + 12 = 26. \]

### Step 3: Rewrite the middle term using these two numbers.
So, the expression becomes:
\[
5x^2 + 10x + 12x + 24.
\]

### Step 4: Factor by grouping.
Group the terms in pairs:
\[
(5x^2 + 10x) + (12x + 24).
\]
Now factor each group:
\[
5x(x + 2) + 12(x + 2).
\]

### Step 5: Factor out the common binomial.
\[
(5x + 12)(x + 2).
\]

So, the factored form of \( 5x^2 + 26x + 24 \) is \( (5x + 12)(x + 2) \).

Would you like more details on this process? Also, here are some related questions to help you practice:

1. How do you handle factoring when the leading coefficient is not 1?
2. Can you factor \( 6x^2 + 17x + 5 \) using a similar method?
3. What are the steps for factoring trinomials where the middle term's sign is negative?
4. What happens if the trinomial cannot be factored using integers?
5. How do you factor a quadratic when the coefficient of \(x^2\) is negative?

**Tip**: Always check your factorization by expanding the factors to ensure they multiply back to the original expression!

Learn how to factor the trinomial 5x^2 + 26x + 24 using the grouping method. This problem involves key algebra concepts such as quadratic equations and factoring trinomials. Suitable for students in Grades 8-10.

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