Is #9x^2 + 42x + 49# a perfect square trinomial and how do you factor it?
We know that
In our case:
To verify whether it fits the pattern, we set the first term of the pattern equal to the first term of the given trinomial:
Then we set the last term of the pattern equal to the last term of the given trinomial:
Taking the square root of both we obtain:
We can use this information to check whether the middle term is true:
The middle term is true, therefore, we conclude that the given trinomial is a perfect square.
We can use the left side of the pattern to factor the given trinomial: