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The trinomial you need to factor is:

\[
x^2 + 3x - 28
\]

To factor this trinomial, we look for two numbers that multiply to give \(-28\) (the constant term) and add up to \(3\) (the coefficient of the middle term, \(x\)).

The pair of numbers that work are \(7\) and \(-4\), since:

\[
7 \times (-4) = -28 \quad \text{and} \quad 7 + (-4) = 3
\]

Now, we can factor the trinomial:

\[
x^2 + 3x - 28 = (x + 7)(x - 4)
\]

So the factored form is:

\[
(x + 7)(x - 4)
\]

You can now submit this as the answer.

Would you like more details on this factoring process?

Here are 5 related questions to deepen your understanding:
1. How can you factor trinomials when the coefficient of \(x^2\) is not 1?
2. What is the difference between factoring and solving a quadratic equation?
3. Can all trinomials be factored into binomials?
4. How does the quadratic formula relate to factoring?
5. How can you check if your factored form is correct?

**Tip:** Always multiply the factored form to verify that it equals the original expression!

Factor the quadratic expression: x^2 + 3x - 28.

Learn how to factor the trinomial x^2 + 3x - 28 by finding two numbers that multiply to give -28 and add up to 3. This step-by-step solution covers key algebraic concepts, suitable for students in Grades 8-10.

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