SOLUTION: By using the remainder theorem, find the reminder for 3(x+4)^2-(1-x)^3 is divided by x. Find the remainder for (2x-1)^3+6(3+4x)^2-10 is divided by 2x+1

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Question 1183411: By using the remainder theorem, find the reminder for 3(x+4)^2-(1-x)^3 is divided by x. Find the remainder for (2x-1)^3+6(3+4x)^2-10 is divided by 2x+1
Found 2 solutions by robertb, ikleyn:
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
Let . Then by the remainder theorem, upon division of f(x) by x, the remainder is f(0).
===> is the remainder.
Now let . Then by the remainder theorem, the remainder is given by , after division by 2x + 1.
Answer by ikleyn(52858)   (Show Source): You can put this solution on YOUR website!
.

(a) By using the remainder theorem, find the reminder for 3(x+4)^2-(1-x)^3 is divided by x.

(b) Find the remainder for (2x-1)^3+6(3+4x)^2-10 is divided by 2x+1
~~~~~~~~~~~~~~~~ 


(a)  According to the remainder theorem, the remainder of  3(x+4)^2-(1-x)^3  when divided by x is the value 

     of this polynomial at x= 0.


     So, we substitute the value of 0 instead of  x  into the polynomial and calculate


            =  = 3*16 - 1 = 48 - 1 = 47.      ANSWER



(b)  According to the remainder theorem, the remainder of  (2x-1)^3+6(3+4x)^2-10  when divided by  (2x+1)  is the value 

     of this polynomial at x= -0.5,  which is the root of the binomial (2x+1).


     So, we substitute the value of  -0.5  instead of  x  into the polynomial and calculate


            =  = -8 + 6 - 10 = -12.      ANSWER

Solved.



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