Question

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The questions are in the attachment........... I want the answers of 12 and 13

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Answer 1

12.

Given p(x) = x^3 - ax^2 + 6x - a, g(x) = x - a.

           
             x^2   +  6
         ------------------------------
x - a)  x^3 - ax^2  +  6x  -  a

          x^3 - ax^2

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

                                    6x  -   a

                                    6x  -   6a

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

                                           5a.


Therefore Quotient = x^2 + 6 and remainder = 5a





(13).

Let f(x) = 2x^3 + x^2 - ax + 2.

Let g(x) = 2x^3 - 3x^2 - 3x + a

Given that f(x) and g(x), when divided by (x - 2), leaves the same remainder. 

f(2) = g(2)

2(2)^3 + (2)^2 - a(2) + 2 = 2(2)^3 - 3(2)^2 - 3(2) + a

16 + 4 - 2a + 2 = 16 - 12 - 6 + a

22 - 2a = -2 + a

-3a = -24

a = 8.


Therefore the value of a = 8.


Hope this helps!