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Solution
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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