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

The remainder after dividing  x4 + 3x3 − 8x2 + 5x − 9 by x + 5 is 16

Step-by-step 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

ok

step-by-step explanation:

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i