Question

Find the quotient and the remainder when :
6x2 + x  − 15 is divided by 3x +5. verify your answer.

Answer 1

`3"x"+5)overline(6"x"^2+"x"−15)(2"x"−3`
              6x²  + 10x
              −     −              
              −9x − 15   
              −9x − 15 
              +     +           
                  ×                  

∴ Quotient = 2x − 3 and remainder = 0

Verification : 

Dividend = Quotient × Divisor + Reminder

= (2x − 3) (3x + 5) + 0

= 6x² + 10x − 9x − 15 + 0

= 6x² − x − 15 which is given