How to factor this expression

Please tell me step by step how to work out:

3a^2+16ab+5b^2

Thanks.

Since the 3 is prime, a 3a goes in one factor and a in the other:

(3a +- ?)(a +- ?)

Since the 5b^2 is positive, the signs are the same. Since the 16ab is positive, they're both plus signs:

(3a + ?)(a + ?)

Since the 5 is prime, the two factors must contain 5b and b. Since 5 times 3 is 15 and 1 times 1 is 1, multiplying the 5b times the 3a and b times a will give you the required 16ab term:

(3a + b)(a + 5b)

Well the only multiples of 3 would be 3 and 1 so you'd start with this:

(3a ) (a )

Since 5b^2 is positive you would be adding in the expression then you'd have this:

(3a + ?) (a + ? )

Then the only multiples of 5 would be 5 and 1. Then you arrange the numbers so that when you foil that they'll end up looking like the original equation.

(3a + 5b) (a + b) would give you 3a^2+ 8ab + 5b^2

Since this doesn't match the original equation then you'd switch the b values which gives you the answer:

(3a + b) (a + 5b)

This one is relatively easy once you note the following:
1. the coefficients of the 1st and 3rd terms are prime.
2. all terms are positive

#1 tells you that you have 3a and a plus 5b and b
#2 tells you that the a and b terms have to all be positive

So, the expression factors as: (3a + b)(a + 5b)
Multiply this out to double check my response gives back the starting expression.

For a polynomial of the form ax^2+bx+c find two factors of a*c (15) that add up b (16).
→ 3,1 for a and 5,1 for b
→(a+5b)(3a+b)
=3a^2+ab+15ab+5b^2
=3a^2+16ab+5b^2

3a^2 + 16ab + 5b^2
= 3a^2 + 15ab + ab + 5b^2
= 3a(a + 5b) + b(a + 5b)
= (3a + b)(a + 5b)