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

Algebra ->  Test -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Let f%28x%29+=+3%28x%2B4%29%5E2-%281-x%29%5E3. Then by the remainder theorem, upon division of f(x) by x, the remainder is f(0).
===> f%280%29+=+3%280%2B4%29%5E2-%281-0%29%5E3+=+3%2A4%5E2+-+1%5E3+=+47 is the remainder.
Now let g%28x%29+=+%282x-1%29%5E3%2B6%283%2B4x%29%5E2-10+. Then by the remainder theorem, the remainder is given by , after division by 2x + 1.

Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
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(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
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(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%2A%280%2B4%29%5E2+-+%281-0%29%5E3 = 3%2A4%5E2+-+1%5E3 = 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


           %282%2A%28-0.5%29-1%29%5E3+%2B+6%2A%283+%2B+4%2A%28-0.5%29%29%5E2+-+10 = %28-2%29%5E3+%2B+6%2A1%5E2+-+10 = -8 + 6 - 10 = -12.      ANSWER

Solved.