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:

                  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).