Part of the Stem Teachers Script
Lesson
Introduction In this lesson you are Mathematicians, in this lesson you are going to learn how to factor a perfect square
10-20 sec going to learn…by
doing/using…
trinomial using the factoring rule for these special polynomials.
Connection You know that… You know that factoring something is just taking a mathematical expression and
(Define Terms/ Building
on Prior Knowledge) breaking it down into simplier factors that can be multiplied together to get the
30-60 sec expression you were factoring. Factoring can always be checked by multiplying out the
factors to see if you get the original expression (so there is no reason to ever get a
factoring problem wrong).
Demonstration I’m going to explain this
1-3 minc idea by showing you…
We are going to be talking about perfect square trinomials. You should be able to see from the
name that we will have perfect square polynomials. A perfect square is something that has two
factors that are the same that when multiplied together you get the perfect square. we can apply
this idea to polynomials by squaring this binomial. Remember this really means we are mulitplying
it by itself so it's really (a+b) times (a+b). When you are multiplying this out remember to multiply
all 4 terms and not just two of them (that is an easy mistake to make). When we multiply it out we
get a^2+2ab +b^2. This is a perfect square trinomial. There is another one as well.
These are almost the same except the subtraction as opposed to addition. This are our
perfect square trinomials. If we can recognize thses patterns it will make factoring much
simiplier. Remember all the a and b are numbers that we don't know yet. Let's take a
look at an example so we can see this.
Application Let’s see how this works in we have x^2-10x+25. First off you have to be able to recognize that it is a perfect square
1-2 min a problem…
trinomial because they will not always tell you. if I made a = x and b = 5 and if i
multiply a and b together I get the middle term. It could fit in the pattern like this. So
now the factored form is (x-5)^2. The reason it is subtraction is because the middle term
is negative. Remember you can always check it to make sure you factored correctly.
This example is a little more tricky. Let's look at this first term. i can write 4x^2 as
(2x)^2 so the a is 2x and I can write 25 as 5^2 and if i multiply a and b together I get the
middle term. With more and more practice you will get better and better at recognizing
these patterns. So now we just have to plug in the terms. its (2x+5)^2. You can tell its
addition because of the addition on the middle term in the original polynomial.
Conclusion So, now you know how In this lesson you learned how to factor a quadratic by using the perfect square trinomial
10-20 sec to…
by…
pattern of factoring.