Question

The binomial (a+5) is a factor of a2+7a+10. What is the other factor?

Answer 1

The answer is (a+2). Let's find factors of a^2 + 7a + 10.

a^2 + 7a + 10 = a^2 + 5a + 2a + 10

= a * a + 5 * a + 2 * a + 2 * 5

= (a * a + 5 * a) + (2 * a + 2 * 5)

= a * (a + 5) + 2 * (a + 5)

= (a + 5) * (a + 2) = (a + 5)(a + 2)

Therefore, a^2 + 7a + 10 = (a + 5)(a + 2).