use synthetic division to solve $(3x^{4}+6x^{3}+2x^{2}+9x + 10)div(x + 2)$. what is the quotient?\n$3x^{3}+12…

Explanation:

Step1: Set up synthetic division

The divisor is (x + 2), so we use (c=-2). The coefficients of the dividend (3x^{4}+6x^{3}+2x^{2}+9x + 10) are (3,6,2,9,10).

Step2: Bring down the first coefficient

Bring down the first - coefficient (3):

- 2	3 6 2 9 10

Step3: Multiply and add

Multiply (-2\times3=-6), add to the second coefficient: (6+( - 6)=0).

- 2	3 6 2 9 10
	- 6

Step4: Repeat multiplication and addition

Multiply (-2\times0 = 0), add to the third coefficient: (2+0 = 2).

- 2	3 6 2 9 10
	- 6 0

Step5: Repeat again

Multiply (-2\times2=-4), add to the fourth coefficient: (9+( - 4)=5).

- 2	3 6 2 9 10
	- 6 0 - 4

Step6: One more time

Multiply (-2\times5=-10), add to the fifth coefficient: (10+( - 10)=0).

- 2	3 6 2 9 10
	- 6 0 - 4 - 10
The quotient is (3x^{3}+0x^{2}+2x + 5=3x^{3}+2x + 5) and the remainder is (0).

Answer:

B. (3x^{3}+2x + 5)