Question

Divide (x^3)-3x^2-13+15 by (x-1)

Answer 1

To divide (x^3)-3x^2-13+15 by (x-1), we can use long division method. The division result is x^2-3x-1/(x-1).

Step-by-step explanation:

To divide (x^3)-3x^2-13+15 by (x-1), we can use long division method:

1. Start by dividing the first term of the dividend, x^3, by the divisor x-1. The answer is x^2.
2. Multiply the divisor x-1 by the answer x^2, which gives x^3-x^2.
3. Subtract x^3-x^2 from the original dividend to obtain the remainder: -3x^2-13+15= -3x^2+2.
4. Bring down the next term -3x^2+2.
5. Divide -3x^2+2 by x-1 to get the next term of the quotient. The answer is -3x.
6. Repeat the process by multiplying the divisor x-1 by the quotient term -3x and subtracting from the remainder.
7. Finally, divide the result of the subtraction, -1, by the divisor x-1 to get the last term of the quotient: -1/(x-1).

Therefore, the division result is: x^2-3x-1/(x-1).