(2u^3-13u^2-8u+7) divided by (u-7) i made a mistake i only need to know the quotient
Do it like long division.
2 u^2 +u -1
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(u-7)| 2 u^3 - 13 u^2 - 8u + 7
2 u^3 - 14 u^2
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u^2 -8u
u^2 -7u
_________
-u + 7
The answer is 2u^2 + u -1
To find the quotient of the polynomial (2u^3 - 13u^2 - 8u + 7) divided by (u - 7) using long division, follow these steps:
1. Write the dividend (2u^3 - 13u^2 - 8u + 7) and the divisor (u - 7) in the long division format. Place the dividend under the long division symbol and the divisor outside the symbol.
2u^2 + u - 1
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u - 7 | 2u^3 - 13u^2 - 8u + 7
2. Begin by dividing the first term of the dividend (2u^3) by the first term of the divisor (u). The result is 2u^2, so write it above the line in the quotient.
2u^2
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u - 7 | 2u^3 - 13u^2 - 8u + 7
3. Multiply the divisor (u - 7) by the quotient term (2u^2). The result is 2u^3 - 14u^2. Write this below the dividend, aligned with the corresponding degree terms.
2u^2 + u - 1
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u - 7 | 2u^3 - 13u^2 - 8u + 7
- (2u^3 - 14u^2)
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\ -u^2 - 8u
4. Subtract the product obtained in step 3 from the corresponding terms of the dividend. Bring down the next term (-8u) from the dividend.
2u^2 + u - 1
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u - 7 | 2u^3 - 13u^2 - 8u + 7
- (2u^3 - 14u^2)
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\ -u^2 - 8u
- (-u^2 + 7u)
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\ -15u + 7
5. Repeat steps 2-4 until you have no more terms to bring down or until the degree of the remaining term in the dividend is less than the degree of the divisor. In this case, the remaining term is (-15u), and its degree is less than the degree of the divisor (u).
2u^2 + u - 1
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u - 7 | 2u^3 - 13u^2 - 8u + 7
- (2u^3 - 14u^2)
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\ -u^2 - 8u
- (-u^2 + 7u)
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\ -15u + 7
- (-15u - 105)
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112
6. The division is now complete. The quotient of (2u^3 - 13u^2 - 8u + 7) divided by (u - 7) is 2u^2 + u - 1.