# (t^3-3t^2+5t-6)divided by (t-2)i made a mistake. i only need to know the quotient

t^2-t+7 Re. 8/(t+2)

## To find the quotient of the polynomial division (t^3-3t^2+5t-6) divided by (t-2), you can use long division. Here's how:

Step 1: Arrange the dividend and divisor in the division format, lining up the like terms:

_________
(t-2) | t^3 - 3t^2 + 5t - 6

Step 2: Divide the first term of the dividend (t^3) by the first term of the divisor (t). Write the result above the line:

t^2
_________
(t-2) | t^3 - 3t^2 + 5t - 6

Step 3: Multiply the divisor (t-2) by the result obtained in Step 2, in this case, t^2. Write the product beneath the dividend, aligning the like terms:

t^2
_________
(t-2) | t^3 - 3t^2 + 5t - 6
- t^3 + 2t^2

Step 4: Subtract the product from the previous step from the corresponding terms of the dividend:

t^2
_________
(t-2) | t^3 - 3t^2 + 5t - 6
- t^3 + 2t^2
________________
- 5t^2 + 5t - 6

Step 5: Bring down the next term from the dividend, which is "5t":

t^2 + 5
_________
(t-2) | t^3 - 3t^2 + 5t - 6
- t^3 + 2t^2
________________
- 5t^2 + 5t - 6
- (- 5t^2 + 10t)

Step 6: Repeat Steps 2-5 until you have no more terms:

t^2 + 5
_________
(t-2) | t^3 - 3t^2 + 5t - 6
- t^3 + 2t^2
________________
- 5t^2 + 5t - 6
- (- 5t^2 + 10t)
_________________
-5t + 6
- (-5t + 10)
_________________
-4

After completing the long division, the quotient is t^2 + 5 - 4/(t - 2).