Divide:

a² + 7a + 12 by a + 4

(a² + 7a + 12) ÷ (a + 4)

= (a² + 3a + 4a + 12) ÷ (a + 4)

= [a(a + 3) + 4(a + 3)] ÷ (a + 4)

= [(a + 3)(a + 4)] ÷ (a + 4)

= $\dfrac{(a + 3)\cancel{(a + 4)}}{\cancel{(a + 4)}}$

= (a + 3)

Hence, (a² + 7a + 12) ÷ (a + 4) = a + 3