Polynomial Long Division: 9x^3+4x^2-6x+1/x^2+6

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Using polynomial long division, evaluate the expression below:
9x3 + 4x2 - 6x + 1
x2 + 6

First, we write our expression in long division format and follow the steps below.

Step 1
1a) Divide the first term of the dividend by the first term of the divisor9x3 ÷ x2 = 9x(3 - 2) = 9x
1b) We multiply that part of the quotient by the divisor9x(x2 + 6) = 9x3 + 54xClick here to see the Math for this Multiplication.
1c) Subtract 9x3 + 54x from 9x3 + 4x2 - 6x + 1 to get 4x2 - 60x + 1Click here to see the Math.

9x
x2 + 69x3 + 4x2 - 6x + 1
9x3 + 54x
4x2 - 60x + 1


Step 2
2a) Divide the first term of the dividend by the first term of the divisor4x2 ÷ x2 = 4x(2 - 2) = 4
2b) We multiply that part of the quotient by the divisor4(x2 + 6) = 4x2 + 24Click here to see the Math for this Multiplication.
2c) Subtract 4x2 + 24 from 4x2 - 60x + 1 to get -60x - 23Click here to see the Math.

9x + 4
x2 + 69x3 + 4x2 - 6x + 1
9x3 + 54x
4x2 - 60x + 1
4x2 + 24
-60x - 23


We have a remainder leftover. We take our answer piece and remainder piece below
Answer = 9x + 4
Remainder piece = Leftover answer divided by our denominator
-60x - 23
x2 + 6