High School Mathematics Extensions/Supplementary/Polynomial Division

Introduction First of all, we need to incorporate some notions about a much more fundamental concept: factoring. We can factor numbers, or even expressions involving variables (polynomials), Factoring is the process of splitting an expression into a product of simpler expressions. It's a technique we'll be using a lot when working with polynomials. Dividing polynomials There are some cases where dividing polynomials may come as an easy task to do, for instance: Distributing, Finally, Another trickier example making use of factors: Reordering, Factoring, One more time, Yielding, 1. Try dividing by . 2. Now, can you factor ? Long division What about a non-divisible polynomials? Like these ones: Sometimes, we'll have to deal with complex divisions, involving large or non-divisible polynomials. In these cases, we can use the long division method to obtain a quotient, and a remainder: In this case: Long division method 1 We first consider the highest-degree terms from both the dividend and divisor, the result is the first term of our quotient. 2 Then we multiply this by our divisor. 3 And subtract the result from our dividend. 4 Now once again with the highest-degree terms of the remaining polynomial, and we got the second term of our quotient. 5 Multiplying... 6 Subtracting... 7 We are left with a constant term - our remainder: So finally: 3. Find some such that is divisible by . deep