hey everyone today we're gonna be talking
about how to complete the square so sometimes
polynomials dont factor so nicely, and in
situations like those we're gonna have to
use this technique called, completing the
square.
I have the steps written up in the corner
here.
So, Step 1 says look at the x term and take
half of its coefficient.
Step 2 says square that number.
Step 3 says Add zero.
And you'll see what I mean by that in a minute.
Now, before we jump into things lets talk
a little bit about what the goal of completing
the square is.
What we want to do is take this polynomial
and break it down into a perfect square plus
a constant.
Alright let's start
So step 1 says look at the x coefficient and
take half of it.
So we have 2 is our x coefficient, we're going
to take half of two, and that will give us
1
step 2 says square it.
so 1 squared equals 1
now we have to add zero. and what I mean by
that is we are going to rewrite our polynomial
but we are going to add this number that we
found, in this case 1, and subtract it, effectively
adding zero. and not changing the problem
So we have x squared plus 2x plus 1 minus
1 plus 3
now if we only look at this first part of
the polynomial
notice that this is a perfect square, and
these two constants here, we can combine,
so if we factor this polynomial and combine
the constants we get x+1 times x+1 plus 2
we can combine them and rewrite this as x+1
squared plus 2
and thats what it means to be a perfect square
now lets look at this example down here
first lets look at the x coefficient and take
half
that is going to give us 3 in this case
then step 2 says square that number
3 squared equals 9
now we have to add zero
so we will rewrite our polynomial as
x squared plus 6x plus 9 minus 9 plus 11
now factor the first three terms and make
a perfect square
they make the perfect square x +3
so this equals x +3 squared plus 2
and that is how to complete the square
I hope this helped and thanks for watching
