How do you divide (x^4+x^2+2) / (x-2) ?

1 Answer
flamespirit919
Apr 27, 2017

x^3+2x^2+5x+10+\frac{22}{x-2}

Explanation:

We have to find what multiplied by x-2 cancels x^4. In this case it is x^3. Multiplying by x^3 we get x^4-2x^3. We can then subtract this from the numerator to get
x^4+x^2+2-(x^4-2x^3)=2x^3+x^2+2

Now we need to find a value that will cancel 2x^3. This value is 2x^2. Multiplying by this we get 2x^3-4x^2. Subtracting we get
2x^3+x^2+2-(2x^3-4x^2)=5x^2+2

The value that will cancel out 5x^2 is 5x. Subtracting we get
5x^2+2-(5x^2-10x)=10x+2

To cancel out 10x we can us 10.
10x+2-(10x-20)=22

Since we can't divide anymore, 22 is the remainder. We add the remainder divided by the denominator to the rest of the terms we got to get
x^3+2x^2+5x+10+\frac{22}{x-2}

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