Question

Find the remainder when f(x)=x^4-3x^2+4 is divided by g(x)=x-2 and verify the result by actual division

Answer 1

GIVEN :

Find the remainder when $f(x)=x^4-3x^2+4$ is divided by g(x)=x-2 and verify the result by actual division

TO FIND :

The remainder when $f(x)=x^4-3x^2+4$ is divided by g(x)=x-2 and verify the result by actual division

SOLUTION :

Given that the functions are $f(x)=x^4-3x^2+4$ is divided by g(x)=x-2 and verify the result by actual division

Put x=2 in f(x) we get

$f(2)=2^4-3(2)^2+4$

=16-12+4

=20-12

=8

⇒ f(2)=8

∴ remainder = 8

Now we can verify it by actual division method, f(x) can be written as $f(x)=x^4+0x^3-3x^2+0x+4$

Now divide f(x) by g(x) as below :

          $x^3+2x^2+x+2$

      _____________________

x-2 ) $x^4+0x^3-3x^2+0x+4$

        $x^4-2x^3$

      _(-)__(+)____

                 $2x^3-3x^2$

                 $2x^3-4x^2$

               _(-)___(+)______

                              $x^2+0x$

                               $x^2-2x$

                          __(-)__(+)______

                                             2x+4

                                             2x-4

                                          _(-)_(+)___

                                                  8

                                          ________

When the given function f(x) is divided by g(x) then the remainder is 8 and it is verified by actual division.

∴ remainder = 8

Answer 2

Answer:

remainder =8

explaination

f(2)=2^4-3(2)+4

=16-12+4

=20-12

=8