Question

Divide the following polynomials 3a^2 + 2a - 7 into 27a^4 + 18a^2 - 2a + 42

Answer 1

9a² - 6a + 31 + [(-106a + 259)/(3a² + 2a - 7)]

Explanation:

9a² - 6a + 31

3a² + 2a - 7 ║27 + 0a³ + 18a² - 2a + 42

-(27 + 18a³ - 63a²)

- 18a³ + 81a² - 2a

-(-18a³ - 12a² + 42a)

93a² - 44a + 42

-(93a² + 62a - 217)

-106a +259 → remainder

Answer: 9a² - 6a + 31 + [(-106a + 259)/(3a² + 2a - 7)]

Answer 2

9a² - 6a + 31
3a² + 2a - 7 ║27
`a^(4)` + 0a³ + 18a² - 2a + 42
-(27
`a^(4)` + 18a³ - 63a²)
- 18a³ + 81a² - 2a
-(-18a³ - 12a² + 42a)
93a² - 44a + 42
-(93a² + 62a - 217)
-106a +259 → remainder

Answer: 9a² - 6a + 31 + [(-106a + 259)/(3a² + 2a - 7)]