How do you divide #(x^2+x-2)/(2x + 4)# using polynomial long division?
As the remainder is zero the division is exact.
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To divide (x^2+x-2) by (2x + 4) using polynomial long division, follow these steps:
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Write the dividend (x^2+x-2) and the divisor (2x + 4) in the long division format.
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2x + 4 | x^2 + x - 2
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Divide the first term of the dividend (x^2) by the first term of the divisor (2x). The result is (1/2)x.
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Multiply the divisor (2x + 4) by the result obtained in step 2, which is (1/2)x. Write the product (x) below the dividend, aligned with the x term.
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2x + 4 | x^2 + x - 2 - (x^2 + 2x)
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Subtract the product obtained in step 3 from the dividend. Write the result (-x - 2) below the line.
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2x + 4 | x^2 + x - 2 - (x^2 + 2x) _________________ -3x - 2
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Bring down the next term from the dividend, which is (-3x). Write it next to the result obtained in step 4.
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2x + 4 | x^2 + x - 2 - (x^2 + 2x) _________________ -3x - 2 - ( -3x - 6)
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Subtract the product obtained in step 5 from the result obtained in step 4. Write the result (4) below the line.
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2x + 4 | x^2 + x - 2 - (x^2 + 2x) _________________ -3x - 2 - ( -3x - 6) _________________ 4
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Since there are no more terms to bring down, the division is complete. The quotient is (1/2)x - 1 and the remainder is 4.
Therefore, (x^2+x-2)/(2x + 4) = (1/2)x - 1 + 4/(2x + 4).
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To divide ( \frac{x^2 + x - 2}{2x + 4} ) using polynomial long division, follow these steps:
- Divide the first term of the numerator by the first term of the denominator: ( \frac{x^2}{2x} = \frac{1}{2}x ).
- Multiply the entire denominator by ( \frac{1}{2}x ): ( \frac{1}{2}x \times (2x + 4) = x^2 + 2x ).
- Subtract the result from the numerator: ( (x^2 + x - 2) - (x^2 + 2x) = -x - 2 ).
- Bring down the next term from the numerator: ( -x - 2 ).
- Divide the leading term of the new polynomial by the first term of the denominator: ( \frac{-x}{2x} = -\frac{1}{2} ).
- Multiply the entire denominator by ( -\frac{1}{2} ): ( -\frac{1}{2} \times (2x + 4) = -x - 2 ).
- Subtract the result from the previous polynomial: ( (-x - 2) - (-x - 2) = 0 ).
The result of the division is ( \frac{1}{2}x - \frac{1}{2} ).
Therefore, ( \frac{x^2 + x - 2}{2x + 4} = \frac{1}{2}x - \frac{1}{2} ).
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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.
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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