Question

find remainder theorem 3x³+3x²+3x+1/x+2​

Answer 1

Step-by-step explanation:

3x³+2x²-19x+6

when x=2

Since the remainder is 0, x = 2 is an actual zero. This means that x - 2 is one of the factors. The numbers on the bottom represent the coefficients of the other factor. Notice that the exponents are reduced by 1. 

3x³ + 2x² - 19x + 6 = (x - 2)(3x² + 8x - 3) 

You can factor 3x² + 8x - 3 further. 

3x³ + 2x² - 19x + 6 = (x - 2)(3x² + 8x - 3) = (x - 2)(3x - 1)(x + 3) 

Set each factor to 0 and solve. 

x - 2 = 0 

x = 2 

3x - 1 = 0 

3x = 1 

3x / 3 = 1 / 3 

x = 1 / 3 

x + 3 = 0 

x = -3 

ANSWER: {-3, 1 / 3, 2}