Divide the polynomials using long division.

Question

(x^3-28x^2-21x+20)/(x+4)

Answer 1

To divide the polynomials using long division, we start by writing the equation in the long division format:

_____________________________
(x+4) | x^3 - 28x^2 - 21x + 20

We will focus on dividing the highest degree term of the numerator, which is x^3, by the highest degree term of the denominator, which is x. The result of this division is x^2, so we write x^2 above the line:

x^2
_____________________________
(x+4) | x^3 - 28x^2 - 21x + 20

Next, we multiply the entire denominator (x+4) by the x^2 we just found, and write the result below the line, lining up like terms:

x^2
_____________________________
(x+4) | x^3 - 28x^2 - 21x + 20
- x^3 - 4x^2

Next, we subtract the new polynomial (x^3 + 4x^2) from the original polynomial (x^3 - 28x^2 - 21x + 20):

x^2
_____________________________
(x+4) | x^3 - 28x^2 - 21x + 20
- x^3 - 4x^2
_________________
-24x^2 - 21x + 20

Now, we repeat the process with the new polynomial (-24x^2 - 21x + 20). We focus on dividing the highest degree term (-24x^2) by the highest degree term (x) in the denominator. The result is -24x, so we write -24x below the line, below the x^2 we already found:

x^2 - 24x
_____________________________
(x+4) | x^3 - 28x^2 - 21x + 20
- x^3 - 4x^2
_________________
-24x^2 - 21x + 20

Again, we multiply the entire denominator (x+4) by the -24x, and write the result below the line, lining up like terms:

x^2 - 24x
_____________________________
(x+4) | x^3 - 28x^2 - 21x + 20
- x^3 - 4x^2
_________________
-24x^2 - 21x + 20
+ 24x^2 + 96x

Next, we subtract the new polynomial (24x^2 + 96x) from the previous polynomial (-24x^2 - 21x + 20):

x^2 - 24x
_____________________________
(x+4) | x^3 - 28x^2 - 21x + 20
- x^3 - 4x^2
_________________
-24x^2 - 21x + 20
+ 24x^2 + 96x
___________________
75x + 20

Now, we repeat the process with the new polynomial (75x + 20). We focus on dividing the highest degree term (75x) by the highest degree term (x) in the denominator. The result is 75, so we write 75 below the line, below the x term we already found:

x^2 - 24x + 75
_____________________________
(x+4) | x^3 - 28x^2 - 21x + 20
- x^3 - 4x^2
_________________
-24x^2 - 21x + 20
+ 24x^2 + 96x
___________________
75x + 20

Finally, we multiply the entire denominator (x+4) by the 75, and write the result below the line, lining up like terms:

x^2 - 24x + 75
_____________________________
(x+4) | x^3 - 28x^2 - 21x + 20
- x^3 - 4x^2
_________________
-24x^2 - 21x + 20
+ 24x^2 + 96x
___________________
75x + 20
- 75x - 300

Now, we subtract the new polynomial (-75x - 300) from the previous polynomial (75x + 20):

x^2 - 24x + 75
_____________________________
(x+4) | x^3 - 28x^2 - 21x + 20
- x^3 - 4x^2
_________________
-24x^2 - 21x + 20
+ 24x^2 + 96x
___________________
75x + 20
- 75x - 300
____________________
320

At this point, we have reached a remainder of 320 with no more terms left in the numerator to divide by the denominator, so our final answer is:

x^2 - 24x + 75 + (320 / (x + 4))

Answer 2

whats that answer?

Answer 3

The final answer is:

x^2 - 24x + 75 + 320/(x + 4)