Find the value of p if the expression px^2-3÷2x+1÷16 is a perfect square ,given that p is constant
Let's start by considering the expression (2x+1)^2 and expanding it:
(2x+1)^2 = 4x^2+4x+1
We can rewrite this as:
4x^2+4x+1 = (4x^2+8x+4) - (4x+3) + 1
= 4(x+1)^2 - (4x+3)
So we can see that if p=4, then px^2-3÷2x+1÷16 will be equal to (2x+1)^2. Therefore, if p=4, the expression would be a perfect square.
Therefore, the value of p is 4.