use synthetic division to find the result when $x^{4}-11x^{3}+28x^{2}-15x + 6$ is divided by $x - 3$. if…
use synthetic division to find the result when $x^{4}-11x^{3}+28x^{2}-15x + 6$ is divided by $x - 3$. if there is a remainder, express the result in the form $q(x)+\frac{r(x)}{b(x)}$.
Answer
Explanation:
Step1: Set up synthetic division
The divisor is $x - 3$, so we use $c=3$. The coefficients of the dividend $x^{4}-11x^{3}+28x^{2}-15x + 6$ are $1,-11,28,-15,6$.
| 3 | 1 | -11 | 28 | -15 | 6 |
|---|---|---|---|---|---|
| 1 |
Step2: Bring down the first coefficient
Bring down the first coefficient 1.
| 3 | 1 | -11 | 28 | -15 | 6 |
|---|---|---|---|---|---|
| 1 |
Step3: Multiply and add
Multiply 3 by 1 to get 3, add to - 11: $-11 + 3=-8$.
| 3 | 1 | -11 | 28 | -15 | 6 |
|---|---|---|---|---|---|
| 3 | |||||
| 1 | -8 |
Step4: Repeat multiply - add
Multiply 3 by - 8 to get - 24, add to 28: $28+( - 24)=4$.
| 3 | 1 | -11 | 28 | -15 | 6 |
|---|---|---|---|---|---|
| 3 | -24 | ||||
| 1 | -8 | 4 |
Step5: Repeat again
Multiply 3 by 4 to get 12, add to - 15: $-15 + 12=-3$.
| 3 | 1 | -11 | 28 | -15 | 6 |
|---|---|---|---|---|---|
| 3 | -24 | 12 | |||
| 1 | -8 | 4 | -3 |
Step6: One more time
Multiply 3 by - 3 to get - 9, add to 6: $6+( - 9)=-3$.
| 3 | 1 | -11 | 28 | -15 | 6 |
|---|---|---|---|---|---|
| 3 | -24 | 12 | -9 | ||
| 1 | -8 | 4 | -3 | -3 | |
| The quotient $q(x)=x^{3}-8x^{2}+4x - 3$ and the remainder $r(x)=-3$, $b(x)=x - 3$. |
Answer:
$x^{3}-8x^{2}+4x - 3-\frac{3}{x - 3}$