Question

please solve this question

Answer 1

(1)


Method - 1:


                    x^2/2   +   x/4   +  7/8
                  ----------------------------------------
2x  +   5)   x^3  +   3x^2   +   3x    +   1  

                 x^3   +  5x^2/2

                 -------------------------------------------

                               x^2/2   +   3x   +   1

                               x^2/2    +  5x/4

                    --------------------------------------

                                                 7x/4   +     1

                                                 7x/4    +   35/8

                     ------------------------------------------------
  
                                                                 -27/8




Method (2) :

Given Equation is f(x) = x^3 + 3x^2 + 3x + 1   ------- (1)

By the remainder theorem,

5 + 2x = 0

x = -5/2.

Substitute in (1), we get

x^3 + 3x^2 + 3x + 1

(-5/2)^3 + 3(-5/2)^2 + 3(-5/2) + 1

-125/8 + 75/4 - 15/2 + 1

$\frac{1 * 8 - 125 + 2 * 75 - 4 * 15}{8}$

-27/8.





(2)

Given Equation is f(x) = x^3 + 3x^2 + 3x + 1  ------ (1)

By the remainder theorem, We get

x + pi = 0

x = -pi.

Substitute x in (1), we get

f(-pi) = (-pi)^3 + 3(-pi)^2 + 3(-pi) + 1

        = -pi^3 + 3pi^2 - 3pi + 1.


This one can also be explained using polynomial division, but u won't understand.




Hope this helps!

Answer 2

Hi,


Please see the attached file!


Thanks