# How do you divide #(7x^4 - 4x^2 – 36x+ 81 )/((x + 9) )#?

#7x^4-4x^2-36+81#

#= (x+9)(7x^3-63x^2+563x-5103)+46008#

I like to long divide the coefficients, not forgetting to include a

Long division of coefficients is similar to long division of numbers.

We find:

#7x^4-4x^2-36+81#

#= (x+9)(7x^3-63x^2+563x-5103)+46008# That is

#(7x^4-4x^2-36+81)# divided by#(x+9)# results in a quotient#(7x^3-63x^2+563x-5103)# with remainder#46008# .

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To divide (7x^4 - 4x^2 – 36x + 81) by (x + 9), you can use long division. Here are the steps:

- Divide the first term of the numerator (7x^4) by the first term of the denominator (x). This gives you 7x^3.
- Multiply the entire denominator (x + 9) by the result from step 1 (7x^3), and write the product (7x^3(x + 9)) below the numerator.
- Subtract the product from the numerator: (7x^4 - 4x^2 – 36x + 81) - (7x^3(x + 9)). Simplify this expression: 7x^4 - 4x^2 – 36x + 81 - 7x^3(x + 9).
- Bring down the next term from the numerator, which is -4x^2.
- Divide the new expression (-4x^2 – 36x + 81) by the first term of the denominator (x). This gives you -4x.
- Multiply the entire denominator (x + 9) by the result from step 5 (-4x), and write the product (-4x(x + 9)) below the expression from step 5.
- Subtract the product from the expression: (-4x^2 – 36x + 81) - (-4x(x + 9)). Simplify this expression: -4x^2 – 36x + 81 + 4x(x + 9).
- Bring down the next term from the numerator, which is -36x.
- Repeat steps 5-7 with the new expression (-36x + 81).
- Bring down the last term from the numerator, which is 81.
- Repeat steps 5-7 with the new expression (81).
- At this point, you have no more terms to bring down. The division is complete.
- The quotient is the sum of the results from each step: 7x^3 - 4x - 36 + (81/(x + 9)).

Therefore, the division of (7x^4 - 4x^2 – 36x + 81) by (x + 9) is equal to 7x^3 - 4x - 36 + (81/(x + 9)).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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