To factorize the quadratic expression \( 2x^2 + 7x + 3 \), you can use the following steps:

### Step 1: Multiply the leading coefficient and the constant term.
Multiply the coefficient of \( x^2 \) (which is 2) by the constant term (which is 3):
\[
2 \times 3 = 6
\]

### Step 2: Find two numbers that multiply to 6 and add up to the middle term (7).
We need two numbers that multiply to 6 and add up to 7. These numbers are 6 and 1 because:
\[
6 \times 1 = 6 \quad \text{and} \quad 6 + 1 = 7
\]

### Step 3: Split the middle term.
Now, rewrite the middle term \( 7x \) as \( 6x + 1x \):
\[
2x^2 + 6x + 1x + 3
\]

### Step 4: Group the terms.
Group the first two terms and the last two terms:
\[
(2x^2 + 6x) + (1x + 3)
\]

### Step 5: Factor each group.
Factor out the greatest common factor from each group:
\[
2x(x + 3) + 1(x + 3)
\]

### Step 6: Factor out the common binomial.
Now, factor out the common binomial factor \( (x + 3) \):
\[
(2x + 1)(x + 3)
\]

Thus, the factorization of \( 2x^2 + 7x + 3 \) is:
\[
(2x + 1)(x + 3)
\]

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. How do you factorize a quadratic equation when the leading coefficient is 1?
2. Can you solve the equation \( 2x^2 + 7x + 3 = 0 \) using the factors?
3. How can you check if a factorization is correct?
4. What is the difference between factorizing and expanding a quadratic expression?
5. How do you factor quadratic expressions with negative coefficients?

**Tip:** When factorizing, always check your answer by multiplying the factors back to the original expression!

Learn how to factorize the quadratic expression 2x² + 7x + 3 using simple steps. This guide explains core algebraic concepts such as splitting the middle term, factorization, and grouping, ideal for students in Grades 9-10.

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