Question

Find the remainder when 4x^3 - 3x^2 + 4x - 2 is divided by (a)x-1 (b)x-2

Answer 1

Let p(x) = 4x³ - 3x² + 4x -2
(a) 
Let x-1 = 0
x = 1
Remainder theorem,
p(1) = 4(1)³ - 3(1)² + 4(1) - 2
        = 4 - 3 + 4 -2
      =3
So, R = 3
(b)
Let x-2 = 0, x= 2
p(2) = 4(2)³ -3(2)² + 4(2) -2
        = 32 - 12 +  8 -2
       = 26
So, remainder is 26
Hope this helps!

Answer 2

when $4x^{3} -3x^{2} +4x4x-2$ is divided by $(x-1)$ The remainder is 3

when $4x^{3} -3x^{2} +4x4x-2$ is divided by $x-2$ The remainder is 26.

Step-by-step explanation:

Given:

• The given expression is$4x^{3} -3x^{2} +4x4x-2$

To find: Find the remainder of the given expression dividing by $(a)x-1, (b)x-2$

Solution:

(i) Find the remainder when the expression $4x^{3} -3x^{2} +4x4x-2$ is divided by $(a)x-1$

      $4x^{2} +x+5$

$\sqrt[x-1]{4x^{3}-3x^{2} +4x-2 }$

  $-(4x^{3} -4x^{2} )$

   ________________

               $x^{2} +4x$

            $-(x^{2} -x)$

   _________________

                      $5x-2$

                   $-(5x-5)$

    _________________

                               $3$

The remainder is 3.

(ii) Find the remainder when the expression $4x^{3} -3x^{2} +4x4x-2$ is divided by $(b) x-2$

       $4x^{2} +5x+14$

$\sqrt[x-2]{4x^{3}-3x^{2} +4x-2 }$

   $-(4x^{3} -8x^{2} )$

   ________________

                $5x^{2} +4x$

             $-(5x^{2} -10x)$

   __________________

                         $14x-2$

                     $-(14x-28)$

     ___________________

                                   $26$

The remainder is 26.

Hence, we get the remainder 3 when $4x^{3} -3x^{2} +4x4x-2$ is divided by $(a)x-1$ also we get the remainder 26 when  $4x^{3} -3x^{2} +4x4x-2$is divided by $(b) x-2$ .