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The given expression is \( c^2 + 3c - 28 \).

To factorise this quadratic expression, we look for two numbers that multiply to give \(-28\) (the constant term) and add to give \(3\) (the coefficient of \(c\)).

These numbers are \(7\) and \(-4\), because:
\[
7 \times (-4) = -28 \quad \text{and} \quad 7 + (-4) = 3.
\]

Thus, the factorised form of \( c^2 + 3c - 28 \) is:
\[
(c + 7)(c - 4).
\]

So, the fully factorised form is:
\[
(c + 7)(c - 4).
\]

Would you like further details on this factorization process or how to verify it?

Here are 5 related questions for you to explore further:
1. How can we verify if the factorization is correct?
2. Can all quadratic expressions be factorised using simple integers?
3. What happens if a quadratic cannot be factorised into integers?
4. How does the quadratic formula help in factorisation?
5. Can we factorise more complex polynomials similarly?

**Tip:** When factorising quadratics, always check the product of the constant term and the middle term's coefficient for a quick hint on finding the correct factors.

Learn how to fully factorise the quadratic expression c^2 + 3c - 28. This step-by-step guide helps you understand factoring by identifying two numbers that multiply to give -28 and add to give 3. Ideal for students in Grades 8-10.

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