Question

1. select the correct equation represented by the division problem.

-2
2
7
13
14
2
-4
-6
-14
3
7
0

1. find the quotient.

2
5
3
8
-2
-5x² - 13x - 34 remainder - 66
-5x³ - 13x² - 34x - 60
5x³ + 13x² + 34x + 66
5x² + 13x + 34 remainder 66
(-2x³ - 7x² - 13x - 14) ÷ (x - 2) = 2x² + 3x + 7
(2x³ + 7x² + 13x + 14) ÷ (x - 2) = 2x² + 3x + 7
(2x³ + 7x² + 13x + 14) ÷ (x + 2) = 2x² + 3x + 7
(x + 2) ÷ (2x³ + 7x² + 13x + 14) = 2x² + 3x + 7

1. find the quotient.

Explanation:

For Question 3:

Step1: Identify dividend & divisor

Synthetic division uses $k=2$, so divisor is $x-2$. The top row $2,7,13,14$ are coefficients of dividend $2x^3+7x^2+13x+14$.

Step2: Match to division equation

The result of synthetic division gives quotient $2x^2+3x+7$ with remainder 0, so $\frac{2x^3+7x^2+13x+14}{x-2}=2x^2+3x+7$.

Step1: Bring down leading coefficient

Bring down the first coefficient: $5$

Step2: Multiply and add (col1)

Multiply $5$ by $2$, add to $3$: $5 \times 2 + 3 = 13$

Step3: Multiply and add (col2)

Multiply $13$ by $2$, add to $8$: $13 \times 2 + 8 = 34$

Step4: Multiply and add (col3)

Multiply $34$ by $2$, add to $-2$: $34 \times 2 + (-2) = 66$

Answer:

$\boldsymbol{(2x^3 + 7x^2 + 13x + 14) \div (x - 2) = 2x^2 + 3x + 7}$

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For Question 4: