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4
avatar+52 

What is the remainder when the polynomial \(g(x) = x^3-14x^2+18x+72\)
is divided by \(x-1\)

 Jun 1, 2021
 #1
avatar+34358 
+3

By doing the long division:

 

                    x^2    - 13x -5       R   77

(x-1) |  x^3 -14x^2  +18x +72

           x^3 -x^2

                 -13x^2  + 8x

                 -13x^2 +13x

                             -5x   + 72

                             -5x   +  5

                                        77

 Jun 1, 2021
 #3
avatar+52 
0

Thanks this really helped!

ThanksForAllHelp  Jun 2, 2021
 #2
avatar+121056 
+3

Thx, EP.....we  can also  apply the Remainder Theorem

 

If a polynomial P(x)  is  divded  by  x - a ,  the  remainder  = P(a) 

 

So....letting  a   =  1 , we  have

 

1^3  - 14(1)^2   + 18(1)  +  72  = 

 

1  -  14   +  90

 

91  - 14   =

 

77      just as EP  found  !!!

 

We can see the logic of this....if  x  =1   were  a root....then P(1)   =   0

 

 

cool cool cool

 Jun 1, 2021
 #4
avatar+52 
0

I really appreciate the help!

ThanksForAllHelp  Jun 2, 2021

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