Math, asked by rinkipatni, 9 months ago

What must be subtracted from 2x⁴ – 5x³ + 5x + 40 so that the result is divisible by 2x – 1?

Answers

Answered by amitnrw
5

Given :   2x⁴ – 5x³ + 5x + 40  

To find : What must be subtracted so that the result is divisible by 2x – 1

Solution:

f(x) =   2x⁴ – 5x³ + 5x + 40  

Remainder Theorem

the result is divisible by 2x – 1   if  f(1/2)  = 0

f(1/2)  = 2 (1/2)⁴ - 5(1/2)³  + 5(1/2) + 40

=> f(1/2) = 1/8  - 5/8  + 5/2  + 40

=> f(1/2) =  42

Hence 42 has to be subtracted from 2x⁴ – 5x³ + 5x + 40 so that the result is divisible by 2x – 1

Another method :

Division method

                     x³ - 2x² - x + 2

2x - 1     _|   2x⁴ – 5x³ + 5x + 40  |_

                   2x⁴ –  x³

                   __________

                             – 4x³ + 5x + 40

                             –  4x³ + 2x²

                             ___________

                                   - 2x² + 5x + 40

                                    - 2x² + x

                                    _____________

                                               4x + 40

                                                4x  - 2

                                               ________

                                                      42

Remainder = 42

Hence 42 must  be subtracted from 2x⁴ – 5x³ + 5x + 40 so that the result is divisible by 2x – 1

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