x rase to 4 minus16 divide by x+2
Answers
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
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.