[MUSIC] Let's work with the factor theorem.

For example, let's determine whether x-3 is a factor of P(x), and we can use the

factor theorem to help us out. Part here.

[SOUND] And the factor theorem, states that a polynomial P has a factor x - r if

and only if r is a 0 or a root of that polynomial.

So we want to use this to determine whether x - 3, is a factor of this

polynomial. So our r here is 3 and we want to compute

p of 3 by plugging in 3 wherever we see and x and see if we get 0 as our answer.

And if we do then yes, x-3 will be a factor of p.

So alright, what is p of 3? This is equal to 2 times 3 cubed minius 5 times 3

squared minus 3 minus 6, which is equal to 2 times 27 - 5 times 9 minus 3.

- 6 or 54 - 45 - 3 - 6. And 54 - 45 is 9.

And then - 3 - 6 is -9. So sure enough, yes, this is equal to 0.

So since P(3) = 0, x - 3 is a factor of P.

Lets see another example. Let's determine whether x plus two is a factor of p.

Again, we will use the factor theorem, which states that x-r will be a factor if

r is zero of p. We want to determine whether x+2, is a

factor of p(x). But what is our r here? X+2 is really x

minus a -2. So be careful here, our r is -2.

So we'll plug in -2 everywhere we see an x here and if we get 0 as an answer then

yes, x plus 2 will be a factor of P. So what is P of -2? This is equal to

negative 2 times negative 2 to the 4th minus 2 times negative 2 cubed plus six

times negative 2 squared minus 5. = -2(16) and then -2(-8) and then 6(4) -

5 = -32. + 16 + 24 - 5.

Now, 16 + 24 = 40, and 40 - 5 = 35, so this is -32.

-32 + 35 = 3 which is not 0. So since P(-2) is not equal to 0, x + 2

is not a factor of P. and this is how we work with the factor

theorem. Thank you, and we'll see you next time.

[SOUND]