What is a perfect square trinomial
Let's first remember what a trinomial is. A polynomial has several terms. A trinomial (as the prefix "tri-" suggests) is a polynomial with three terms. When we're dealing with perfect squares, it means we're dealing with squaring binomials. Continue on to learn how we go about factoring a trinomial.
How to factor perfect square trinomials
One good way to recognize if a trinomial is perfect square is to look at its first and third term. If they are both squares, there's a good chance that you may be working with a perfect square trinomial.
Let's say we're working with the following: x2+14x+49. Is this a perfect square trinomial? Looking at the first term, we've got x2, which is a square. The last term is 49. It is also a square since when you multiply 7 by 7, you'll get 49. Therefore 49 can also be written as 72. The next step to identifying if we've got a perfect square is to see if we are able to get the middle term of 14x when we have x2and 72 to work with.
In the case of a perfect square, the middle term is the first term multiplied by the last term, and then multiplied by 2. In other words, the perfect square trinomial formula is:
a2±ab+b2. We're now trying to see if we can get the middle term of 2ab.
Since we've got our a term as x, and our b term as 7, our 2ab becomes 2∙7∙x. That gives us a total of 14x, which is the middle term in x2+14x+49! Therefore, we can rewrite the question as (x+7)2through factoring perfect square trinomials. You've solved a perfect square trinomial! You're now ready to apply trinomial factoring to some practice problems.
Factor the perfect square
We know that this is a perfect square, and all we're asked is to factor it. Therefore, just take a look at the first and last term and find what they are squares of. It'll give us:
Factor the perfect square
Take out the common factor 3
Factor the x2−10x+25 and get the final answer:
Find the square of a binomial:
You can square it and it will become what we have here:
So the first term:
Square of −3x2=9x4
The third term:
The middle term is the multiplication of original 1st and 2nd term, and then times 2
Then times 2:
So the final answer:
To double check your answers, this online calculator will help you factor a polynomial expression. Use it as a reference, but make sure you learn how to properly go through the steps to answering a perfect square trinomial question.
Wasn't quite sure on the concepts covered in this chapter? Perhaps you may want to go back and review how to find common factors of polynomials or how to factor by grouping. Also read up on solving polynomials with unknown coefficients, and the intro to factoring polynomials.