Question 23192: please help! 22 years since I did this. Trying to help my son.
[(4x^3 - 2x^2 + x -9) / (x-2)]
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Do you remember synthetic division or long division? Synthetic division is easier if you can do it this way. Write down the coefficients of the numerator, and since the denominator is x-2, perform the division with (the opposite sign) +2.
2_| 4 -2 1 -9
-> __________
Bring down the first number which is 4:
2_| 4 -2 1 -9
-> __________
- -> 4
Multiply 4 times 2, which is 8 and place under the -2:
2_| 4 -2 1 -9
-> ___8_______
- -> 4
Add -2 + 8 = 6:
2_| 4 -2 1 -9
-> ___8_______
- -> 4 6
Multiply 6 times 2 = 12 and place under the 1:
2_| 4 -2 1 -9
-> ___8_12_____
- -> 4 6
Add 1 + 12 = 13:
2_| 4 -2 `1 ` -9
-> ___8_12_____
- -> 4 6 13
Multiply 13 times 2 which is 26, and place under the -9:
2_| 4 -2 `1 `-9
-> ___8_12_26__
- -> 4 6 13
Add the -9+26 which is 17
2_| 4 -2 `1 `-9
-> ___8_12_26__
- -> 4 6 13 17
The last number is the remainder of the quotient, which is traditionally written as a numerator divided by the divisor. The first three numbers (that is, 4, 6, and 13) are the coefficients of the answer. The answer always begins with an exponent one less than the highest power of the original problem. In this case, the problem begins with x^3, so the answer will begin with x^2:
Final answer, with coefficients of 4, 6, and 13, with a remainder of 17:
No Extra Charge: If you substitute the value x=2 (that you divided by!) into the original problem:
 you get the remainder every time. It gives me a GREAT way to check my answer, before I post an error! There's nothing like a public error to teach humility!!
R^2 at SCC
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