How do you divide #(x^3+12x^212x+15) / (x31) # using polynomial long division?
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To divide (x^3+12x^212x+15) by (x31) using polynomial long division, follow these steps:

Arrange the dividend and divisor in descending order of exponents: x^3+12x^212x+15 divided by x31.

Divide the first term of the dividend (x^3) by the first term of the divisor (x). The result is x^2.

Multiply the divisor (x31) by the quotient obtained in step 2 (x^2). The result is x^3+31x^2.

Subtract the product obtained in step 3 from the dividend (x^3+12x^212x+15) to get the new dividend: 12x^212x+15(x^3+31x^2).

Bring down the next term of the dividend (12x) and repeat steps 24.

Divide the first term of the new dividend (12x^2) by the first term of the divisor (x). The result is 12x.

Multiply the divisor (x31) by the quotient obtained in step 6 (12x). The result is 12x^2372x.

Subtract the product obtained in step 7 from the new dividend (12x^212x+15(x^3+31x^2)) to get the new dividend: 384x+15.

Bring down the next term of the new dividend (15) and repeat steps 24.

Divide the first term of the new dividend (384x) by the first term of the divisor (x). The result is 384.

Multiply the divisor (x31) by the quotient obtained in step 10 (384). The result is 384x+11904.

Subtract the product obtained in step 11 from the new dividend (384x+15(384x+11904)) to get the remainder: 11889.
The quotient is x^2+12x+384 and the remainder is 11889.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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