Question

What minimum must be added to 2x3 - 3x3 + 6x + 7 so that the resulting polynomial will be divisible by x2-4x+8

Please do this quick!!!

Answer 1

THE MINIMUM THAT MUST BE ADDED TO POLYNOMIAL $2X^3-3X^2+6X+7$ IS $-10X+33$

Step-by-step explanation:

To calculate the minimum required to add in the given polynomial $2X^3-3X^2+6X+7$ so that it will be completly divisible by the $2x^2-4x+8$

we have to devide the $2X^3-3X^2+6X+7$ by $2x^2-4x+8$

NOW ,

                           $\dfrac{2x^3-3x^2+6x+7}{x^2-4x+8}$

                    $\frac{2x(x^2-4x+8) +5(x^2-4x+8) +10x-33}{x^2-4x+8}$

                            $2X+5+\frac{10X-33}{X^2-4X+8}$

      On deviding remainder is 10x-33

• NOW TO CALCULATE THE MINIMUM REQUIRED IS TO MAKE COMPLETLY DIVISIBLE WE HAVE TO SUBTRACT THE REMAINDER.

THEREFORE THE MINIMUM REQUIRED TO ADD IS         -(10X-33)

   THAT IS $-10X+33$