OP - Polynomial Division Lesson

Polynomial Division

Operations on Functions
Operation	Definition	Example: f(x) = 5x, g(x) = x + 2
Add	h(x) = f(x) + g(x)	h(x) = 5x + (x + 2) = 6x + 2
Subtract	h(x) = f(x) - g(x)	h(x) = 5x - (x + 2) = 4x - 2
Multiply	$h\left(x\right)=f\left(x\right)\cdot g\left(x\right)$	$h\left(x\right)=5x\left(x+2\right)=5x^2+10x$
Divide	$h\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}$	$h\left(x\right)=\frac{5x}{x+2}$

Operations can be done with functions just like with expressions.

Also, in division remember that denominators cannot be zero, so g(x)  ≠ 0.  These "combinations" of functions use the same properties you learned in previous modules. You can find the domain of each by determining what values can be used for x, the same as in previous modules. Always simplify your answers, where possible.

Division and Zero

Zero divided by a nonzero number

$0\div K=0\:or\:\frac{0}{K}\:=0\:\left(as\:long\:as\:K\:is\:not\:equal\:to\:0\right)$

Remember: Zero on top of the fraction is ok!!!

A number divided by zero

$N\div0$ is undefined (we cannot divide by 0)

Remember: Zero on the bottom of the fraction NO $\longrightarrow\frac{N}{0}$ is undefined.

Watch the following teaching videos to show you how addition, subtraction, multiplication, and division is used when given different functions.

Polynomial Division using Long Division

Long Division with polynomials is just like the long division that you learned in elementary school but now we will also be using variables. Divide the first term of the dividend by the first term of the divisor, then multiply and subtract. You will have a new polynomial to repeat the original process with. If there is a remainder other than zero, write the remainder as a fraction with the remainder as the numerator and the original divisor as the denominator.

Watch the following teaching videos to help you understand the process of Dividing Polynomials using Long Division.

Polynomial Division using Synthetic Division

Synthetic division is a method that removes the variables during the division process but puts them back at the end to recreate a polynomial expression. Instead of divide and subtract, you multiply and add. (Any remainders other than zero are treated the same way they are in long division, rewritten as a fraction with the remainder as the numerator and the divisor as the denominator.)

Watch the following teaching videos to help you understand the process of Dividing Polynomials using Synthetic Division.

 

Now it is time for you to complete the Dividing Polynomials Self-Assessment.

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