If c is a constant such that 9x^2+10x+c is equal to the square of a binomial, then what is c?
Since the first term of 9x2 + 10x + c is 9, in factored form it must look like: (3x + a)2.
Expanding (3x + a)2 = 9x2 + 6ax + a2
This means that 10x = 6ax ---> 6a = 10 ---> a = 10/6 ---> a = 5/3
Placing this value of a into (3x + a)2 ---> (3x + 5/3)2 ---> 9x2 + 10x + 25/9
So: c = 25/9.