(t^3-3t^2+5t-6)divided by (t-2)
t^2
t-2! t^3-3t^2+5t-6
t^3-2t^2
then t
t-2 t^2 +5t -6
t^2 -10t
then 15
t-2 15t -6
15t -30
then remainder 24
check my work
4t + 8 = 3 ( 3.5t)
To check your work, let's perform the division and see if the steps are correct.
We have the polynomial t^3 - 3t^2 + 5t - 6 divided by t - 2.
Step 1: Divide t^3 by t to get t^2. Write t^2 above the line.
t^2
___________
t - 2 | t^3 - 3t^2 + 5t - 6
t^3 - 2t^2
___________
+
Step 2: Multiply t - 2 by t^2 to get t^3 - 2t^2. Write this below the line and subtract it from the original polynomial.
t^2
___________
t - 2 | t^3 - 3t^2 + 5t - 6
- (t^3 - 2t^2)
___________
+ t^2 + 5t - 6
Step 3: Bring down the next term, which is 5t. We now have t^2 + 5t.
t^2 + 5
___________
t - 2 | t^3 - 3t^2 + 5t - 6
- (t^3 - 2t^2)
___________
+ t^2 + 5t - 6
t^2 + 5t
_________
+
Step 4: Divide t^2 + 5t by t - 2. This gives t - 10 as the quotient. Write t - 10 above the line.
t^2 + 5
___________
t - 2 | t^3 - 3t^2 + 5t - 6
- (t^3 - 2t^2)
___________
+ t^2 + 5t - 6
- (t^2 + 5t)
_________
- 6
Step 5: Bring down the next term, which is -6. We now have -6.
t^2 + 5
___________
t - 2 | t^3 - 3t^2 + 5t - 6
- (t^3 - 2t^2)
___________
+ t^2 + 5t - 6
- (t^2 + 5t)
_________
- 6
- 6
_________
+
Step 6: Divide - 6 by t - 2. This gives us - 3 as the remainder.
t^2 + 5
___________
t - 2 | t^3 - 3t^2 + 5t - 6
- (t^3 - 2t^2)
___________
+ t^2 + 5t - 6
- (t^2 + 5t)
_________
- 6
- ( - 6)
_________
0
Since the remainder is 0, it indicates that our division is correct. Therefore, the answer is t^2 + 5 as the quotient, and there is no remainder.
Your work seems to be incorrect since you obtained a remainder of 24. Please double-check your steps.