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### Course: Algebra 2>Unit 4

Lesson 1: Dividing polynomials by x

# Polynomial division introduction

When we divide the polynomial p(x) by q(x) we are basically asking "what should we multiply by q(x) to get p(x)?" If this sounds familiar, it's because it's very similar to dividing numbers! In this introduction we see how some quotients end up as a polynomial, while other times we have a remainder and cannot express the quotient as a polynomial. This is very similar to quotients of integers!

## Want to join the conversation?

• I am confused by the conclusion that x cannot = -1. Lets say we STARTED the function f(x) = x+2. There would be no reason to not use -1. I understand that in this example we arrive at x-2 by simplifying a function that WOULD have a problem with x = -1, BUT whether or not we start with the unsimplified function and reduce it to x+2 or just come up with x+2 to start with, the end resulting graph of f(x) = x+2 would look the same, right?
• Not exactly. This is where the concept of "holes" comes in. Basically a single point on a graph that doesn't exist. Here is a super simple example.

x/x simplifies to 1. Of course tht is just a horizontal line at y = 1. since we started with x/x thee is actually a hole at x=0. So it is actually pretty important what you start with. The starting expression determines your domain, even if things cancel out. If you have a graphing calculator you will be able to see that if you graph x/x and try to tell what x=0 is you will get that it is undefined, while everywhere else it is 1.
• what grade do most students learn this in?
• I think in 10th, maybe 11th this is alg. 2
• Still don’t fully understand this, any ‘better/easier to understand’ formulas for finding the answers with polynomial division, maybe an easier formula.
• i am answering a problem(devide each polynomial by the given binomial.

(64x³-192x²+5x-15)÷(x-2)
how do i solve this?
• So is this similar to factoring polynomials?
• The first step he shows you, factoring would be needed to solve it and im a bit late sry
• he used long division to solve it, will we be learning that later? I don't really understand it.
• Yes, in lesson 2.
• Hey Sal? Can you do a video on Descartes Rule of Signs? Thanks!
• at how is it factorized
• Am I in the right place for Mrs. Green’s class? I can’t tell if I’m doing the right lessons and it’s giving me a lot of anxiety.
• What is the missing number in the series?

1, 16, 81, __, 625, 1296

im having a issue understanding how you get 1 to the power of 4 and so forth can someone explain please?
(1 vote)
• When we say any number to the 4th power, it just means that number multiplied by itself four times. So, 1^4 (one to the fourth power) is 1*1*1*1.
1^1 = 1*1*1*1 = 1
2^4 = 2*2*2*2 = 16
3^4 = 3*3*3*3 = 81
since this fits the pattern shown in your problem, it is logical that the next number would be 4^4
4^4 = 4*4*4*4 = 256