use long division to divide x^3+x^2-2x+14 by x+3
To divide x^3 + x^2 - 2x + 14 by x + 3 using long division, follow these steps:
Step 1: Write the dividend (x^3 + x^2 - 2x + 14) and the divisor (x + 3).
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x + 3 | x^3 + x^2 - 2x + 14
Step 2: Divide the first term of the dividend (x^3) by the first term of the divisor (x).
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x + 3 | x^3 + x^2 - 2x + 14
- (x^3 + 3x^2)
Step 3: Subtract the result (x^2) from the second term of the dividend (x^2), and bring down the next term (-2x).
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x + 3 | x^3 + x^2 - 2x + 14
- (x^3 + 3x^2)
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- 2x + 14
Step 4: Divide the first term of the new dividend (-2x) by the first term of the divisor (x).
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x + 3 | x^3 + x^2 - 2x + 14
- (x^3 + 3x^2)
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- 2x + 14
- (- 2x - 6)
Step 5: Subtract the result (- 2) from the third term of the new dividend (-2x), and bring down the last term (14).
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x + 3 | x^3 + x^2 - 2x + 14
- (x^3 + 3x^2)
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- 2x + 14
- (- 2x - 6)
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20
Step 6: Since there are no more terms to bring down, the division is complete. The quotient is x^2 - 2x - 2, and the remainder is 20.
Therefore, x^3 + x^2 - 2x + 14 divided by x + 3 equals x^2 - 2x - 2 with a remainder of 20.