Polynomial long division question

Question

 When 3x²-5x+c is divided by x+k, the quotient is 3x+1 and the remainder is 3. Find c and k.

Answer 1

3x² - 5x + c =  (x + k)(3x + 1) + 3 = 3x² + x + 3kx + k + 3

 

SUbtract 3x² from both sides and collect terms on the right

 

-5x + c = (3k + 1)x + k + 3

 

3k + 1 = -5 => k = -2

 

c= k + 3 = -2 + 3 = -1

 

You should plug the values of c and k into the original problem and check that it works correctly!