(t^3-3t^2+5t-6)divided by (t-2)i made a mistake. i only need to know the quotient
No problem! To find the quotient of the polynomial (t^3 - 3t^2 + 5t - 6) divided by (t - 2), you can use the long division method. Here's how you can do it:
1. Start by writing the dividend (t^3 - 3t^2 + 5t - 6) inside the long division symbol and the divisor (t - 2) outside the symbol.
________________________
t - 2 | t^3 - 3t^2 + 5t - 6
2. Look at the highest power term in the dividend, which is t^3. Divide it by the highest power term in the divisor, which is t, and write the result (t) above the division line.
t
________________________
t - 2 | t^3 - 3t^2 + 5t - 6
3. Multiply the entire divisor (t - 2) by the t term you just found (t * (t - 2) = t^2 - 2t) and write the result below the dividend, aligned with the like terms.
t
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t - 2 | t^3 - 3t^2 + 5t - 6
- (t^3 - 2t^2)
4. Subtract the expression you just obtained (t^2 - 2t) from the first term in the dividend (t^3 - 3t^2) and write the result (-t^2 + 5t) below the line.
t
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t - 2 | t^3 - 3t^2 + 5t - 6
- (t^3 - 2t^2)
_________________
- t^2 + 5t
5. Bring down the next term from the dividend, which is 5t, and place it next to the difference you just found (-t^2 + 5t).
t
________________________
t - 2 | t^3 - 3t^2 + 5t - 6
- (t^3 - 2t^2)
_________________
- t^2 + 5t
+ 5t
6. Repeat the process by dividing the highest power term (-t^2) in the new expression (-t^2 + 5t) by the divisor (t).
The result of this division will be (-t).
7. Multiply the entire divisor (t - 2) by the new term you found (-t * (t - 2) = -t^2 + 2t) and write the result below the line.
t - 1
________________________
t - 2 | t^3 - 3t^2 + 5t - 6
- (t^3 - 2t^2)
_________________
- t^2 + 5t
+ 5t
- (-t^2 + 2t)
8. Subtract the expression you just obtained (-t^2 + 2t) from the current difference (- t^2 + 5t) and write the result (3t) below the line.
t - 1
________________________
t - 2 | t^3 - 3t^2 + 5t - 6
- (t^3 - 2t^2)
_________________
- t^2 + 5t
+ 5t
- (-t^2 + 2t)
_________________
3t
9. Since there are no more terms in the dividend, the division process is completed.
The quotient of (t^3 - 3t^2 + 5t - 6) divided by (t - 2) is given by t - 1.
Therefore, the quotient is t - 1.