Question

For what value of `n` is `x^2-10x+n` a perfect square trinomial?

Answer 1

`n=5^2 = 25` since every perfect square trinomial is of the form `a^2+2ab+b^2`

Explanation:

Every perfect square trinomial is of the form:

`a^2+2ab+b^2 = (a+b)^2`

In the given example, `a=x` and `2ab = 2x*b = -10x`,

so `b=(-10x)/(2x) = -5` and `n=b^2=(-5)^2 = 5^2 = 25`.