Question

Find the polynomial of least degree that should be subtracted from
p(x) = x3 - 2x2 + 3x + 4 so that it is exactly divisible by
g(x) = x2 - 3x +1.​

Answer 1

Given: p(x) = x^3 - 2x^2 + 3x + 4  and  g(x) = x^2 - 3x +1

To find: The polynomial of least degree that should be subtracted from

p(x) so that it is exactly divisible by  g(x) .

Solution:

• Now we have given two equations :

                  p(x) = x^3 - 2x^2 + 3x + 4  and  g(x) = x^2 - 3x +1

• By division method, we get:

                                 

           x^2 - 3x +1  )  x^3 - 2x^2 + 3x + 4    (  x + 1

                                 x^3 - 3x^2 + x

                                (  -        +        -   )

                                           x^2  + 2x  + 4

                                           x^2  -  3x  + 1

                                          (  -        +     -   )

                                                      5x + 3

• So 5x + 3 is the polynomial.

Answer:

             So 5x + 3 must be subtracted from p(x) so that it is exactly divisible by  g(x) .

Answer 2

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