Dividing Polynomials

[julesjanker]

Hi, I understand how to divide polynomials synthetically just fine but I just realized it only works with linear so I do need to know how to long divide too!
Can someone show me the clear steps and explain how to solve:

x^4 - 15x^3 + 12x -10 ÷ x^2 -4

So far the only thing I understood was x^4 ÷ x^2 = x^2 which you put in your first space...
my text book then tells me to multiply and I'm so lost!

 

[tkhunny]

It is almost like numeric long division. The ONLY difference is that you get to pick any Real Number at each stage, not just integers [0,9].

Really, think about numeric ling division and the base 10 positional system. You will see the similarity.

 

[Mrspi]

Hi, I understand how to divide polynomials synthetically just fine but I just realized it only works with linear so I do need to know how to long divide too!
Can someone show me the clear steps and explain how to solve:

x^4 - 15x^3 + 12x -10 ÷ x^2 -4

So far the only thing I understood was x^4 ÷ x^2 = x^2 which you put in your first space...
my text book then tells me to multiply and I'm so lost!

Write your divisor in standard form:

x[sup:32q5arcs]4[/sup:32q5arcs] - 15x[sup:32q5arcs]3[/sup:32q5arcs] + 0 x[sup:32q5arcs]2[/sup:32q5arcs] + 12 x - 10

Now, use either long division or synthetic division... I think maybe your error might be in omitting a power of x.

 

[chrisr]

You can also write

x^4-15x^3+12x-10 = (x^2-4)(x^2+bx+10/4) as x^2 by x^2 is x^4 and -4(10/4) is -10

so 12x = -4bx so b = -3

but when you multiply out we find an " x squared term" of -3x^2/2

therefore there is a remainder or you've missed a term,
as it does not divide in exactly