Question

x rase to 4 minus16 divide by x+2​

Answer 1

Step-by-step explanation:

(x⁴-16)/(x+2)

(x²+4)(x²-4)/(x+2)

(x²+4)(x-2)(x+2) / (x+2)

(x²+4)(x-2)

x³-2x²+4x-8

Answer 2

Quotient is x³-2x²+4x-8, no remainder.

To solve : Perform synthetic division?

Coefficient of

4th degree term 1

3rd degree term 0

2nd degree term 0

1st degree term 0

0th degree term -16

Now write down from 4th to 0th, with spaces

  1   0   0   0   -16

To divide by x+2, write -2 on the left

-2  |   1   0   0   0   -16

Next step, follow my drawing.

-2  |   1   0   0   0   -16

    |______________

Steps of synthetic division

First, highest degree term stays same.

-2  |   1   0   0   0   -16

    |______________

        1

Next, multiply -2 on that and raise to right top.

-2  |   1   0   0   0   -16

    |____-2_________

        1

The number stays same.

-2  |   1   0   0   0   -16

    |____-2_________

        1    -2

Now, iterate it!!

-2  |   1   0   0   0   -16

    |       -2   4   -8   16

        1   -2   4   -8  | 0

Therefore, quotient is x³-2x²+4x-8, leaving no remainder.