1. **State the problem:** Factorise the quadratic expression $x^2 + 5x - 14$. 2. **Recall the formula and rules:** To factorise a quadratic expression of the form $ax^2 + bx + c$, we look for two numbers that multiply to $ac$ and add to $b$. 3. **Identify coefficients:** Here, $a=1$, $b=5$, and $c=-14$. 4. **Find two numbers:** We need two numbers that multiply to $1 \times (-14) = -14$ and add to $5$. 5. **List factor pairs of -14:** $(1, -14)$, $(-1, 14)$, $(2, -7)$, $(-2, 7)$. 6. **Check sums:** - $1 + (-14) = -13$ - $-1 + 14 = 13$ - $2 + (-7) = -5$ - $-2 + 7 = 5$ 7. The pair $-2$ and $7$ multiply to $-14$ and add to $5$. 8. **Rewrite the middle term:** $$x^2 + 5x - 14 = x^2 - 2x + 7x - 14$$ 9. **Group terms:** $$ (x^2 - 2x) + (7x - 14) $$ 10. **Factor each group:** $$ x(x - 2) + 7(x - 2) $$ 11. **Factor out the common binomial:** $$ (x + 7)(x - 2) $$ **Final answer:** $$\boxed{(x + 7)(x - 2)}$$