How do you long divide #(12x³11x²27x9) / (4x+3)#?
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To long divide (12x³  11x²  27x  9) by (4x + 3), follow these steps:

Divide the first term of the dividend (12x³) by the first term of the divisor (4x). This gives you 3x².

Multiply the entire divisor by the result from step 1 (3x²), which gives you 12x³ + 9x².

Subtract this result from the original dividend, which gives you 20x²  27x  9.

Bring down the next term from the original dividend, which is 9.

Repeat the process by dividing the first term of the new dividend (20x²) by the first term of the divisor (4x), which gives you 5x.

Multiply the entire divisor by 5x, giving you 20x²  15x.

Subtract this result from the new dividend, giving you 12x  9.

Since the degree of the remaining term (12x) is less than the degree of the divisor, you have the remainder.
So, the result of the long division is 3x²  5x  3 with a remainder of 9/(4x + 3).
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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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