Answer:
The remainder after dividing x4 + 3x3 − 8x2 + 5x − 9 by x + 5 is 16
Explanation:
We have to divide x4 + 3x3 − 8x2 + 5x − 9 by x+5
First of all we solve the first term of the dividend.
We have the divisor x+5
If we multiply it by x^3 than we get the first term of our dividend.
x^3(x+5) = x^4+5x^3
x4 + 3x3 − 8x2 + 5x − 9
x^4+5x^3
- -
___________________
-2x^3-8x^2+5x-9
Now we have the first term of dividend as -2x^3
Now we will multiply x+5 by -2x^2 to get the first term
-2x^2(x+5) = -2x^3-10x^2
-2x^3-8x^2+5x-9
-2x^3-10x^2
+ +
______________
2x^2+5x-9
Now the first term of the dividend is 2x^2
So we will multiply x+5 by 2x
2x(x+5)= 2x^2+10x
2x^2+5x-9
2x^2+10x
- -
_________
-5x -9
Now the dividend we have is -5x-9
We will multiply x+5 by -5
-5(x+5) = -5x-25
-5x -9
-5x-25
+ +
______
16
Thus the remainder after dividing x4 + 3x3 − 8x2 + 5x − 9 by x + 5 is 16....