# How do you divide #( -3x^3+ 3x^2-30x-72 )/(x + 1 )#?

The fastest method is probably synthetic division; giving:

#{: (,,color(blue)(-3),color(blue)(+3),color(blue)(-30),color(blue)(-72)), (,,,+3,-6,+36), (xx (color(red)(-)color(green)(1)),"|",bar(color(cyan)(-3)),bar(color(cyan)(+6)),bar(color(cyan)(-36)),bar(color(brown)(-36))) :}#

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To divide (-3x^3 + 3x^2 - 30x - 72) by (x + 1), you can use long division. Here are the steps:

- Divide the first term of the dividend (-3x^3) by the first term of the divisor (x). This gives you -3x^2.
- Multiply the divisor (x + 1) by the quotient (-3x^2), which gives you -3x^3 - 3x^2.
- Subtract this result (-3x^3 - 3x^2) from the dividend (-3x^3 + 3x^2 - 30x - 72). This gives you 6x^2 - 30x - 72.
- Bring down the next term from the dividend, which is -30x.
- Divide the first term of the new dividend (6x^2) by the first term of the divisor (x). This gives you 6x.
- Multiply the divisor (x + 1) by the new quotient (6x), which gives you 6x^2 + 6x.
- Subtract this result (6x^2 + 6x) from the new dividend (6x^2 - 30x - 72). This gives you -36x - 72.
- Bring down the next term from the dividend, which is -72.
- Divide the first term of the new dividend (-36x) by the first term of the divisor (x). This gives you -36.
- Multiply the divisor (x + 1) by the new quotient (-36), which gives you -36x - 36.
- Subtract this result (-36x - 36) from the new dividend (-36x - 72). This gives you -36.
- There are no more terms to bring down, so the division is complete.

The quotient is -3x^2 + 6x - 36, and the remainder is -36.

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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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