Is #x^2 − 10x + 25# a perfect square trinomial and how do you factor it?
It is a perfect square! The square is
In a perfect square trinomial, the function
If we try to fit the problem statement into this format, we would have to figure out what value
Solving the first equation:
There are two solutions for a there because the square of either a negative or positive real number is always positive.
Let's look at possible solutions for the second equation:
This agrees with one of the solutions for the first equation, meaning that we have a match!
We can now write out the perfect square as:
A quadratic can be written as
There is a quick way to check whether it is a perfect square trinomial.
#(b/c)^2 = c#?
In a perfect square trinomial, a special relationship exists between
In this case:
The relationship exists, so this is a perfect square trinomial.