The expression \( 2x^2 + 15x + 28 \) can be factored by finding two numbers that multiply to \( 2 \times 28 = 56 \) and add up to \( 15 \).

Let's follow the steps to factor this quadratic expression:

1. Multiply the coefficient of \( x^2 \) (which is 2) and the constant term (which is 28), giving us \( 2 \times 28 = 56 \).
2. We now need two numbers that multiply to 56 and add up to 15. These numbers are 7 and 8 since:
   \[
   7 \times 8 = 56 \quad \text{and} \quad 7 + 8 = 15
   \]
3. Now, rewrite the middle term \( 15x \) using these numbers:
   \[
   2x^2 + 7x + 8x + 28
   \]
4. Factor by grouping:
   \[
   (2x^2 + 7x) + (8x + 28)
   \]
5. Factor out the greatest common factor (GCF) from each group:
   \[
   x(2x + 7) + 4(2x + 7)
   \]
6. Now, factor out \( (2x + 7) \):
   \[
   (2x + 7)(x + 4)
   \]

So, the factored form of \( 2x^2 + 15x + 28 \) is:
\[
(2x + 7)(x + 4)
\]

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would you solve \( 2x^2 + 15x + 28 = 0 \)?
2. Can every quadratic expression be factored this way?
3. What is the quadratic formula, and how can it be applied to this expression?
4. How do you check if your factorization is correct?
5. How can completing the square help in solving quadratics?

**Tip:** Always check your factorization by multiplying the factors back together to ensure they give the original quadratic expression.

Learn how to factor the quadratic equation 2x^2 + 15x + 28 step by step. This example involves factoring by grouping and is perfect for students in Grades 8-10. Explore key algebraic concepts and understand the process behind quadratic factorization.

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