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Find long division (x^4+6x^2+2)/(x^2+5)

Solution:
Your problem `->` long division (x^4+6x^2+2)/(x^2+5)


Final Solution
 ```x^2``+``0x``+``1`  
`color{blue}{x^2+5}``` `x^4``+` `0x^3``+` `6x^2``+` `0x``+` `2`  
 ```x^4``+``5x^2` `x^2 xx (color{blue}{x^2+5})`
 `` `0x^3``+` `x^2``+` `0x``+` `2`  
 ```0x^3``+``0x` `0x xx (color{blue}{x^2+5})`
 `` `x^2``+` `2`  
 ```x^2``+``5` `color{green}{1} xx (color{blue}{x^2+5})`
 `-` `3`  

Final answer `= "Quotient" + (color{Magenta}{"Remainder"})/(color{blue}{"Divisor"})`.
`:.` Final answer = `x^2+0x+1 + (color{Magenta}{-3})/(color{blue}{x^2+5})`
 
Here, Divisor = `x^2+5`
Dividend = `x^4+6x^2+2`
Quotient = `x^2+0x+1`
Remainder = `-3`



Step by step solutions
Step - 1 :
1. Divide the first term of the dividend by the first term of the divisor : `(x^4)/(x^2)=color{green}{x^2}`

2. Write down the calculated result `color{green}{x^2}` in the upper part of the table.

3. Multiply it by the divisor `color{green}{x^2} xx (color{blue}{x^2+5})=color{red}{x^4+5x^2}`

4. Subtract this result from the dividend
`(x^4+0x^3+6x^2+0x+2)-(color{red}{x^4+5x^2})=color{Magenta}{0x^3+x^2+0x+2}`

 ```x^2`  
`color{blue}{x^2+5}``` `x^4``+` `0x^3``+` `6x^2``+` `0x``+` `2`  
 ```x^4``+``5x^2` `color{green}{x^2} xx (color{blue}{x^2+5})`
 `` `0x^3``+` `x^2``+` `0x``+` `2`  


Step - 2 :
1. Divide the first term of the dividend by the first term of the divisor : `(0x^3)/(x^2)=color{green}{0}`

2. Write down the calculated result `color{green}{0}` in the upper part of the table.

3. Multiply it by the divisor `color{green}{0} xx (color{blue}{x^2+5})=color{red}{0x^3+0x}`

4. Subtract this result from the remainder
`(0x^3+x^2+0x+2)-(color{red}{0x^3+0x})=color{Magenta}{x^2+2}`

 ```x^2``+``0x`  
`color{blue}{x^2+5}``` `x^4``+` `0x^3``+` `6x^2``+` `0x``+` `2`  
 ```x^4``+``5x^2` `x^2 xx (color{blue}{x^2+5})`
 `` `0x^3``+` `x^2``+` `0x``+` `2`  
 ```0x^3``+``0x` `color{green}{0x} xx (color{blue}{x^2+5})`
 `` `x^2``+` `2`  


Step - 3 :
1. Divide the first term of the dividend by the first term of the divisor : `(x^2)/(x^2)=color{green}{1}`

2. Write down the calculated result `color{green}{1}` in the upper part of the table.

3. Multiply it by the divisor `color{green}{1} xx (color{blue}{x^2+5})=color{red}{x^2+5}`

4. Subtract this result from the remainder
`(x^2+2)-(color{red}{x^2+5})=color{Magenta}{-3}`

 ```x^2``+``0x``+``1`  
`color{blue}{x^2+5}``` `x^4``+` `0x^3``+` `6x^2``+` `0x``+` `2`  
 ```x^4``+``5x^2` `x^2 xx (color{blue}{x^2+5})`
 `` `0x^3``+` `x^2``+` `0x``+` `2`  
 ```0x^3``+``0x` `0x xx (color{blue}{x^2+5})`
 `` `x^2``+` `2`  
 ```x^2``+``5` `color{green}{1} xx (color{blue}{x^2+5})`
 `-` `3`  







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