Answer:
(a + 4)(a + 6)
Step-by-step explanation:
f(a) = a² + 10a + 24
I think you are asking us to factor the quadratic.
1. Multiply the leading coefficient and the constant
1 × 24 = 24
2. Find two numbers that multiply to give 24 and add to give 10.
Possible pairs are 1, 24; 2, 12; 3, 8; 4, 6
Start with the numbers near the end of the list.
By trial and error, you will find that 4 and 6 work:
4 × 6 = 24 and 4 + 6 = 10
3. Rewrite 10a as 4a + 6a
a² +4a + 6a +24
4. Factor by grouping the first two and the last two terms
a(a + 4) + 6(a + 4)
5. Distribute the a + 4
(a + 4)(a + 6)
a² + 10a + 24 = (a + 4)(a + 6)
