Question

Use synthetic division to find the quotient and remainder. Express your answer as a polynomial.

1. 2x^3-11x^2+13x-21*x-3

2. 3x^3+7x^2-13x+10*x+2

3. 2x^3+13x^2-21x+9*x-1

4. 7x^3-8x+16/x-2

5. 8x^4-14x^3-71x^2-10x+24/x-4

Answer 1

1. 2x³ - 11x² + 13x - 21 ÷ x - 3

x - 3 = 0 ⇒ x = 3

3 | 2 -11 13 -21

| ↓ 6 -15 -6

2 -5 -2 -27

1. Answer: 2x² - 5x - 2 -
`(27)/(x - 3)`

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2. 3x³ + 7x² - 13x + 10 ÷ x + 2

x + 2 = 0 ⇒ x = -2

-2 | 3 7 -13 10

| ↓ -6 -2 30

3 1 -15 40

2. Answer: 3x² + x - 15 +
`(40)/(x + 2)`

3. 2x³ + 13x² - 21x + 9 ÷ x - 1

x - 1 = 0 ⇒ x = 1

1 | 2 13 -21 9

| ↓ 2 15 -6

2 15 -6 3

3. Answer: 2x² + 15x - 6 +
`(3)/(x - 1)`

4. 7x³ + 0x² - 8x + 16 ÷ x - 2

x - 2 = 0 ⇒ x = 2

2 | 7 0 -8 16

| ↓ 14 28 40

7 14 20 56

4. Answer: 7x² + 14x + 20 +
`(56)/(x - 2)`

5. 8x⁴ - 14x³ - 71x² - 10x + 24 ÷ x - 4

x - 4 = 0 ⇒ x = 4

4 | 8 -14 -71 -10 24

| ↓ 32 72 4 -24

8 18 1 -6 0

5. Answer: 8x³ + 18x² + x - 6