Question

score on last try: 0 of 1 pt. see details for more. at least one scored part is incorrect. jump to first changable incorrect part. next question get a similar question you can retry this question below find the quotient and remainder using synthetic division for: \\(\frac{x^{3}+8x^{2}+14x + 7}{x + 2}\\) the quotient is \\(\boxed{}\\) the remainder is \\(\boxed{}\\) question help: video 1 video 2 read 1 written example 1 submit question

Explanation:

Step1: Identify root of divisor

Set $x+2=0$, so $x=-2$.
List coefficients of dividend: $1, 8, 14, 7$.

Step2: Bring down leading coefficient

Bring down $1$.

Step3: Multiply and add

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

Step4: Multiply and add

Multiply $6 \times (-2) = -12$, add to $14$: $14 + (-12) = 2$.

Step5: Multiply and add

Multiply $2 \times (-2) = -4$, add to $7$: $7 + (-4) = 3$.

Step6: Form quotient and remainder

The first three results are coefficients of quotient (degree 2): $1, 6, 2$. The last result is remainder.

Answer:

The quotient is $x^2 + 6x + 2$
The remainder is $3$