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

 

 

When x^4+6x^3-ax^2-45x-15 is divided by x^2-x-6 the remainder is 3. What is a?

 Dec 9, 2018
 #1
avatar+94501 
+2

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

 

We can use some synthetic division to solve this

 

 

5   [  1   0      30       - c   ]

             5      25      275

        ________________

        1    5    55       275 - c

 

So

 

275 - c = 5     implies that  c = 270

 

 

cool cool cool

 Dec 9, 2018
 #2
avatar+94501 
+2

When x^4+6x^3-ax^2-45x-15 is divided by x^2-x-6 the remainder is 3. What is a?

 

Haven't done one like this before......!!!!

 

                        x^2  + 7x+ (13 - a)

x^2 - x  - 6   [   x^4 + 6x^3 - ax^2    -   45x     -    15 ]

                        x^4 - x^3 -  6x^2

                       _____________________________

                               7x^3 + (6 - a)x^2 - 45x

                               7x^3 -     7x^2      -42x

                               ___________________________ 

                                          (13 - a)x^2 - 3x          - 15

                                          (13 - a)x^2 - (13 -a)x - 6(13 - a) 

                                         ___________________________

                                                              (10 - a)x  - 15 + 6(13 - a)

 

So

 

-15 + 6(13 - a) = 3

 

-15 + 78 - 6a = 3

 

63 - 6a = 3

 

-6a = -60

 

 a = 10

 

Check here to see that this is true : 

 

https://www.wolframalpha.com/input/?i=%5B+x%5E4+%2B+6x%5E3+-+10x%5E2+-+45x+%C2%A0-%C2%A0+15%5D+%2F+%5B+x%5E2+-+x+-6%5D

 

 

cool cool cool

 Dec 9, 2018
edited by CPhill  Dec 9, 2018

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