Question

P(x)=2x

4

−x

3

+2x

2

−6P, left parenthesis, x, right parenthesis, equals, 2, x, start superscript, 4, end superscript, minus, x, cubed, plus, 2, x, squared, minus, 6

What is the remainder when P(x)P(x)P, left parenthesis, x, right parenthesis is divided by (x-2)(x−2)left parenthesis, x, minus, 2, right parenthesis?

Answer 1

GIVEN :

The polynomial equation is $P(x)=2x^4-x^3+2x^2-6$

TO FIND :

The remainder when P(x) is divided by x-2

SOLUTION :

Given polynomial is $P(x)=2x^4-x^3+2x^2-6$

The given polynomial  can be written as

$P(x)=2x^4-x^3+2x^2+0x-6$

By using Long Division method  we can find the remainder when P(x) is divided by x-2

             $2x^3+x^2+4x+8$

       ___________________________

x-2  ) $2x^4-x^3+2x^2+0x-6$

        $2x^4-2x^3$

     _(-)__(+)__________

                $x^3+2x^2$

                $x^3-2x^2$

          __(-)__(+)______________

                       $4x^2+0x$

                       $4x^2-8x$

                 __(-)___(+)____________

                               8x-6  

                               8x-16

                          _(-)__(+)_________

                                    10

                        ________________

∴ the remainder when $P(x)=2x^4-x^3+2x^2-6$ is divided by x-2 is 10.

Answer 2

Answer:26

Step-by-step explanation:

For x-2, x would be equal to 2,

so 2(2)^4 -(2^3)+2(2^2)-6

=26