Question

Find the remainder when f(x)=x power 3-2x power 2-5x+4 is divided by g(x)=x-2 and verify the result of actual division.

Answer 1

Solution :-

1 - 2x = 0

- 2x = - 1

2x = 1

x = 1/2

p(x) = x³ - 6x² + 2x - 4

p(1/2) = (1/2)³ - 6*(1/2)² + 2*(1/2) - 4

= 1/8 - 6*(1/4) + 1 - 4

= 1/8 - 6/4 + 1 - 4

= 1/8 - 3/2 + 1 - 4

Taking L.C.M. of the denominators and then solving it.

= (1 - 12 + 8 - 32)/8

= - 35/8

Remainder is - 35/8

Now, actual division.

                          - 6x² - 1

                         _________________

               1 - 2x )      x³ - 6x² + 2x - 4  (

                            12x³ - 6x²   

                          -        +

                        ______________

                          - 11x³     + 2x - 4

                                        + 2x - 1

                                        -      +

                        _______________  

                        - 11x³  - 3

                        _______________

Remainder is - 11x³ - 3

Verification : 

 

⇒ - 11x³ - 3

⇒ - 11*(1/2)³ - 3

⇒ - 11*1/8 - 3

⇒ - 11/8 - 3/1

⇒ Taking L.C.M. of the denominator and then solving it.

⇒ (- 11 - 24)/8

⇒ - 35/8

Verified.