Question

49 find the quotient and remainder using synthetic division for: $\frac{x^{3}+8x^{2}+13x + 4}{x + 2}$ the quotient is the remainder is question help: video 1 video 2 read 1 written example 1 message instructor

Explanation:

Step1: Set up synthetic division

The divisor is $x + 2$, so we use $- 2$ for synthetic division. The coefficients of the dividend $x^{3}+8x^{2}+13x + 4$ are $1,8,13,4$.

Step2: Bring down the first coefficient

Bring down the first coefficient $1$.

-2	1	8	13	4
	1

Step3: Multiply and add

Multiply $-2$ by $1$ to get $-2$, add to $8$: $8+( - 2)=6$.

-2	1	8	13	4
	1	6

Step4: Repeat multiply - add

Multiply $-2$ by $6$ to get $-12$, add to $13$: $13+( - 12)=1$.

-2	1	8	13	4
	1	6	1

Step5: Final multiply - add

Multiply $-2$ by $1$ to get $-2$, add to $4$: $4+( - 2)=2$.

-2	1	8	13	4
	1	6	1	2

The numbers $1,6,1$ are the coefficients of the quotient polynomial and $2$ is the remainder. The quotient polynomial is $x^{2}+6x + 1$ (since the original polynomial was of degree 3, the quotient is of degree 2).

Answer:

The quotient is $x^{2}+6x + 1$
The remainder is $2$