Question

The polynomial y= x^4 + 3x^3 - 83x^2+15x-440 can be written as the product of three factors. two of the factors are (x-8) and (x+11). find the third factor.

Answer 1

To find the third factor, we can use polynomial division or synthetic division to divide the given polynomial by the product of the two known factors:

First, we set up the division:
```
x^2 + 4x - 40
______________________
x-8 | x^4 + 3x^3 - 83x^2 + 15x - 440
-x^4 + 8x^3
_____________
11x^3 - 83x^2
-11x^3 + 88x^2
____________
5x^2 + 15x
-5x^2 + 40x
__________
-25x - 440
25x + 200
___________
-240
```

As the result of the division is -240, we can write the third factor as (x^2 + 4x - 40).