Long division x^2-3x+5 divided by x+1
To divide the polynomial x^2 - 3x + 5 by x + 1 using long division, follow these steps:
1. Write the divisor (x + 1) and the dividend (x^2 - 3x + 5) in standard form:
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x + 1 | x^2 - 3x + 5
2. Divide the first term of the dividend (x^2) by the first term of the divisor (x). The result is the first term of the quotient, x. Write it above the division line:
x
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x + 1 | x^2 - 3x + 5
3. Multiply the entire divisor (x + 1) by the first term of the quotient (x) and write the result underneath the dividend, aligning like terms:
x
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x + 1 | x^2 - 3x + 5
x^2 + x
4. Subtract the multiplied terms from the dividend:
x
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x + 1 | x^2 - 3x + 5
- (x^2 + x)
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-4x + 5
5. Bring down the next term from the original dividend (in this case, -4x + 5):
x - 4
6. Repeat the steps: Divide the new dividend (-4x + 5) by the divisor (x + 1).
x - 4
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x + 1 | x^2 - 3x + 5
- (x^2 + x)
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-4x + 5
-( -4x - 4)
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9
7. The remainder is 9, and there are no more terms to bring down. Thus, the final result is:
x - 4 + 9/(x + 1)
Therefore, the polynomial x^2 - 3x + 5 divided by x + 1 is equal to x - 4 with a remainder of 9.