Synthetic Division-Algebra 2-Dividing Polynomials

Welcome to moomoomath today we will learn how to complete division which is how you divide two polynomials.
In this math problem, we have a cubic polynomial divided by a linear polynomial which means it has a degree of one.
In order for the division to work it the polynomial needs to be to the first degree and needs a lead coefficient of one. It is easier than long division. Step one is we want to figure out what k is. What is the 0 ?
Take x plus 3 and set it equal to 0
We know the zero is negative 3
We take negative 3 and place it in a box
Next take the polynomial we are dividing into and we will write the lead coefficients.
We have a 1 a positive 2 a 6 and negative 9
I will write these out
Next we will divide.
Notice all variables are gone.
I will draw a line, and step one of division is to bring down the coefficient of 1
Now multiply the negative 3 and write your answer.
Now add the column of numbers
Now repeat the process
negative 3 times 1 equals 3
Now add and it equal negative 3
Now add negative 9 and positive 9 and get a remainder of 0
I have created a depressed polynomial
We divided a cubic function by a linear function
When you divide you get an x squared
So my first term is a squared term
I next write x squared negative x negative 3
and that is my polynomial
You can write it as x squared negative x negative 3 and that is your polynomial when you divide.
I will give you another example of division.
You have 3x cubed plus 2 x squared minus 5 divided by x minus 2
You will place positive 2 in the box
Next, we write our coefficients in order to divide
We are missing our linear term.
We have to put a placeholder there.
I call these polynomials with a hole in them.
3 2 0 and negative 5
We multiply 2 by these coefficients and bring down the terms.
3 times 6, add 8, multiply by 16 and add 16 and add 27
The answer is 3x squared plus 8x plus 16
The remainder we will add and leave it as a fraction of 27 over x minus 2
That is how you complete division of polynomials.

[MooMooMath]

Learn the steps for synthetic division. I have taught this for years in my Algebra 2 class.