Question

divide $4x^{4}+4x^{3}-4x^{2}-4$ by $x - 3$. give your answer in the form $q(x)+\frac{r(x)}{d(x)}$. fill in the table below to complete the synthetic division.* quotient =

Explanation:

Step1: Set up synthetic division

For dividing by $x - 3$, we use $c = 3$. The coefficients of the polynomial $4x^{4}+4x^{3}-4x^{2}+0x - 4$ are $4,4,-4,0,-4$.

Step2: Bring down the first coefficient

Bring down the first coefficient $4$.

Step3: Multiply and add

Multiply $3\times4 = 12$, then add to the next coefficient: $4 + 12=16$. Multiply $3\times16 = 48$, add to the next coefficient: $-4+48 = 44$. Multiply $3\times44=132$, add to the next coefficient: $0 + 132=132$. Multiply $3\times132 = 396$, add to the last coefficient: $-4+396 = 392$.
The synthetic - division table (from left - to - right, top - to - bottom) is filled as follows:

	4	4	- 4	0	- 4
	4	16	44	132	392

The quotient $Q(x)=4x^{3}+16x^{2}+44x + 132$ and the remainder $R(x)=392$, and $D(x)=x - 3$.

Answer:

$4x^{3}+16x^{2}+44x + 132+\frac{392}{x - 3}$