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When  \(x^3 +30x -c\)is divided by \(x-5\) the remainder is\(5\). What is \(c\)?

 Jan 17, 2021
 #1
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Long division

 

 

      ______x2__+5x_  +55_______

x-5 |    x^3          + 30x  -c

          x^3  - 5x^2  

                   5x^2  + 30x -c

                   5x^2  - 25x

                               55x -c

                               55x - 275

                                      -c + 275

 

-c + 275 = 5     (the remainder)

-c = -  270

c = 270                     (if I made no mistakes....check it!)

 Jan 17, 2021
 #2
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Faster solution:

The remainder theorem tells us that the remainder is the value of x^3+30x-c when x = 5.

Therefore, 

\((5)^3+30(5)-c=5\\ 125+150-c=5\\ 275-c=5\\ c=270\)

Same answer as guest :)

textot  Jan 17, 2021
 #3
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I like tt's method better....I didn't think of that !   surprise

Guest Jan 17, 2021

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