How do you divide #(x^3 + x^2 +4x 6) / (x^2 3x +2) # using polynomial long division?
The quotient is
Now let's divide that long way.
Consequently,
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To divide (x^3 + x^2 + 4x  6) by (x^2  3x + 2) using polynomial long division, follow these steps:

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

Multiply the entire divisor (x^2  3x + 2) by the result obtained in step 1 (x). The result is x^3  3x^2 + 2x.

Subtract the result obtained in step 2 from the dividend (x^3 + x^2 + 4x  6) to get the new dividend. The new dividend is 4x^2 + 2x  6.

Repeat steps 13 with the new dividend (4x^2 + 2x  6) and the divisor (x^2  3x + 2).

Divide the first term of the new dividend (4x^2) by the first term of the divisor (x^2). The result is 4x.

Multiply the entire divisor (x^2  3x + 2) by the result obtained in step 5 (4x). The result is 4x^3  12x^2 + 8x.

Subtract the result obtained in step 6 from the new dividend (4x^2 + 2x  6) to get the new dividend. The new dividend is 14x^2 + 6x  6.

Repeat steps 13 with the new dividend (14x^2 + 6x  6) and the divisor (x^2  3x + 2).

Divide the first term of the new dividend (14x^2) by the first term of the divisor (x^2). The result is 14.

Multiply the entire divisor (x^2  3x + 2) by the result obtained in step 9 (14). The result is 14x^2  42x + 28.

Subtract the result obtained in step 10 from the new dividend (14x^2 + 6x  6) to get the remainder. The remainder is 48x  34.
Therefore, the quotient is x + 4 and the remainder is 48x  34.
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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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