Question

The remainder after dividing x4 + 3x3 − 8x2 + 5x − 9 by x + 5 is

Answer 1

(x^4+3x^3-8x^2+5x-9)/(x+5)

x^3    remainder -2x^3-8x^2+5x-9
-2x^2 remainder 2x^2+5x-9
2x      remainder -5x-9
-5      remainder 16

(x+5)(x^3-2x^2+2x-5)+16/(x+5)

so the remainder after division is:

16/(x+5)

Answer 2

Answer:

16 is the remainder of the division.

Step-by-step explanation:

The given equation is $x^{4} + 3x^{3} -8x^{2} + 5x - 9$ and we have to divide this expression by x = (-5)

We can find the remainder by synthetic division

-5 |     1      3     -8       5     (-9)  

               -5      10    -10     25

      ---------------------------------------

         1      -2     2      -5      16

We can rewrite the expression as $(x+5)(x^{3}-2x^{2}+2x-5)+16$

Therefore, remainder of the division is 16.