(2u^3-13u^2-8u+7) divided by (u-7) i made a mistake i only need to know the quotient
To find the quotient of the polynomial (2u^3 - 13u^2 - 8u + 7) divided by (u - 7), you can use polynomial long division. Here are the steps to find the quotient:
Step 1: Arrange the dividend and divisor in descending order of powers of u:
2u^3 - 13u^2 - 8u + 7 ÷ (u - 7)
Step 2: Divide the first term of the dividend (2u^3) by the first term of the divisor (u).
The result is 2u^2 since 2u^3 ÷ u = 2u^2.
Step 3: Multiply the divisor (u - 7) by the quotient obtained in the previous step (2u^2).
(2u^2) x (u - 7) = 2u^3 - 14u^2.
Step 4: Subtract the product obtained in the previous step from the dividend, and write the result below:
2u^3 - 13u^2 - 8u + 7
- (2u^3 - 14u^2)
-------------------------
u^2 - 8u + 7
Step 5: Repeat the steps from Step 2 to Step 4 with the new dividend (u^2 - 8u + 7) and the divisor (u - 7).
Step 6: Divide the first term of the new dividend (u^2) by the first term of the divisor (u).
The result is u since u^2 ÷ u = u.
Step 7: Multiply the divisor (u - 7) by the quotient obtained in the previous step (u).
(u) x (u - 7) = u^2 - 7u.
Step 8: Subtract the product obtained in the previous step from the new dividend, and write the result below:
u^2 - 8u + 7
- (u^2 - 7u)
------------------
-u + 7
Step 9: Repeat the steps from Step 2 to Step 4 with the new dividend (-u + 7) and the divisor (u - 7).
Step 10: Divide the first term of the new dividend (-u) by the first term of the divisor (u).
The result is -1 since -u ÷ u = -1.
Step 11: Multiply the divisor (u - 7) by the quotient obtained in the previous step (-1).
(-1) x (u - 7) = -u + 7.
Step 12: Subtract the product obtained in the previous step from the new dividend, and write the result below:
-u + 7
- (-u + 7)
-----------------
0
Step 13: Since the new dividend is 0, the division is complete, and the quotient is 2u^2 + u - 1.
Therefore, the quotient of the polynomial (2u^3 - 13u^2 - 8u + 7) divided by (u - 7) is 2u^2 + u - 1.