Question

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

Answer 1

Answer:

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.

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Answer 2

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:

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

By long division, we have:

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

                     x^3 - 3x^2 + x

                     ( -      +         - )

                                x^2 - 4x + 1

                                x^2 - 3x + 1

                               ( -      +         - )

                                          - x

So the remainder is -x

Answer:

               So -x should be subtracted from p(x)  so that it is exactly divisible by  g(x).