I need help on factoring monomials in quadratic form.

Question

The problem is:

a² + 17a + 16
I know that the first step is to multiply 16 times the coefficient of "a", which is 1. I get 16.
Now I have to fill in factors that when multiplied, equal 16, but when added, equal 17.

So now I have 16 x 1 = 16
and 16 + 1 = 17.

And now I have to fill in the addition factors to make a² + 16a + 1a + 16.

I am just confused as to what to do next to solve the problem.

Answer 1

from your
a² + 16a + 1a + 16 use grouping
a(a+16) + 1(a+16)
=(a+16)(a+1)

you could also have arranged your terms this way
a² + 1a + 16a + 16
=a(a+1) + 16(a+1)
=(a+1)(a+16)

Answer 2

Oh, okay! I understand now. Thank you!