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

Hello from MrBillDoesMath!

(a+2)

Discussion:

Suppose  

a^2 + 7a + 10 = (a+5) (a + b)

Then

a^2 + 7a + 10 =  a^2 + (ab + 5a) + 5b            => factor "a" from rhs, 2nd term

a^2 + 7a + 10 =  a^2 + (b + 5)a + 5b

so 5b = 10  => b = 2

Hence

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

Thank you,

MrB