Question

Find the remainder when p(x)=x 3 -6x 2 +2x-4 ​​ is divided by (1-2x) by remainder theorem and verify the result by 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.

Answer 2

Answer:

substitute

Step-by-step explanation:

there it is ...