https://file.aiquickdraw.com/mathbot/file/1726692731878a8p77kdo.jpg

The given equation to factor is:

\[
21x^2 + 48x + 27
\]

To factor this trinomial, we will use factoring by grouping or other relevant methods.

### Step 1: Multiply the coefficient of \(x^2\) and the constant term
\[
21 \times 27 = 567
\]

### Step 2: Find two numbers that multiply to 567 and add up to 48 (the coefficient of \(x\))
The pair that works is 27 and 21 because:
\[
27 \times 21 = 567 \quad \text{and} \quad 27 + 21 = 48
\]

### Step 3: Rewrite the middle term using these two numbers
\[
21x^2 + 21x + 27x + 27
\]

### Step 4: Factor by grouping
Group the first two and the last two terms:
\[
(21x^2 + 21x) + (27x + 27)
\]

Factor out the greatest common factor (GCF) from each group:
\[
21x(x + 1) + 27(x + 1)
\]

### Step 5: Factor out the common binomial factor
\[
(21x + 27)(x + 1)
\]

### Step 6: Simplify
\[
21x + 27 = 3(7x + 9)
\]
Thus, the factored form is:
\[
3(7x + 9)(x + 1)
\]

Therefore, the factorized form of \(21x^2 + 48x + 27\) is:

\[
3(7x + 9)(x + 1)
\]

Would you like further details on any of the steps? 

Here are some related questions:
1. How do you factor quadratic equations by grouping?
2. What are other methods to factor trinomials?
3. How can you identify when a quadratic is not factorable using integers?
4. What is the importance of factoring in solving quadratic equations?
5. How do you apply the quadratic formula if factoring is difficult?

**Tip:** Always check your factors by expanding them to ensure the original equation is obtained.

Learn how to factor the quadratic expression 21x^2 + 48x + 27. This solution covers factoring by grouping, relevant algebraic concepts, and simplification steps for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation