Divide using long division. Check your answer.
(x^3+3x^2-x+4)/(x-1)
Here is the long division of (x^3+3x^2-x+4)/(x-1):
x^2 + 4x + 3
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x - 1 | x^3 + 3x^2 - x + 4
- ( x^3 - x^2 )
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4x^2 - x + 4
- ( 4x^2 - 4x)
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3x + 4
- ( 3x - 3)
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7
The quotient is x^2 + 4x + 3 and the remainder is 7.
Therefore, (x^3+3x^2-x+4)/(x-1) = x^2 + 4x + 3 + 7/(x-1)
To divide (x^3 + 3x^2 - x + 4) by (x - 1) using long division, follow these steps:
Step 1: Divide the first term of the dividend (x^3) by the divisor (x - 1). The result is x^2, which is written above the line.
x^2
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x - 1 | x^3 + 3x^2 - x + 4
Step 2: Multiply the divisor (x - 1) by the result obtained in the previous step (x^2). Write the product (x^2 * (x - 1) = x^3 - x^2) below the line and subtract it from the dividend.
x^2
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x - 1 | x^3 + 3x^2 - x + 4
- (x^3 - x^2)
____________
4x^2 - x
Step 3: Bring down the next term from the dividend, which is 4x^2. Write it next to the remaining term (-x) to form (4x^2 - x).
x^2 +
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x - 1 | x^3 + 3x^2 - x + 4
- (x^3 - x^2)
_______________
4x^2 - x
Bring down 4x^2:
x^2 +
___________
x - 1 | x^3 + 3x^2 - x + 4
- (x^3 - x^2)
_______________
4x^2 - x
- (4x^2 - x)
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0
Step 4: The division is complete. The quotient is x^2, and the remainder is 0.
Therefore, (x^3 + 3x^2 - x + 4) divided by (x - 1) equals x^2 with no remainder.