Question

Divide x^3-4x^2-4x+16 by x+2​

Answer 1

Answer:

x^2−6x+8

Step-by-step explanation:

x^3−4x^2−4x+16/x+2

=x^3−4x^2−4x+16/x+2

=(x+2)(x−2)(x−4)/x+2

=x^2−6x+8

Answer 2

Method-1 :

p(x) = x³ - 4x² - 4x + 16

g(x) = x + 2

Let ,

g(x) = 0

⇒ x + 2 = 0

⇒ x = - 2

Sub. x value in p(x) ,

⇒ p(-2) = (-2)³ - 4(-2)² - 4(-2) + 16

            = - 8 - 16 + 8 + 16

            = 0

So , ( x³ - 4x² - 4x + 16 ) is divisible by ( x + 2 )

Method-2 : ( To find quotient )

x + 2 ) x³ - 4x² - 4x + 16 ( x² - 6x + 8

          x³ + 2x²

         (-)__(-)___

               - 6x² - 4x

               - 6x² - 12x

               _(-)__(-)___

                          8x + 16

                          8x + 16

                          (-)_(-)__              

                                 0

So , Quotient = x² - 6x + 8

⇒ ( x³ - 4x² + 16 ) = ( x + 2 ) ( x² - 6x + 8 )