Question

WORTH 45!!!
Use division to show that (x+5) is a factor given y= 2x^3 - x^2 - 41x + 70

Answer 1

To show that (x+5) is a factor of y= 2x^3 - x^2 - 41x + 70 using division, we can use long division as follows:

```
2x^2 - 11x + 14
_______________________
x + 5 | 2x^3 - x^2 - 41x + 70
-(2x^3 + 10x^2)
---------------
-11x^2 - 41x
(-11x^2 - 55x)
-------------
14x + 70
(14x + 70)
--------
0
```

We can see that (x+5) evenly divides into 2x^3 - x^2 - 41x + 70, with no remainder. Therefore, we have shown that (x+5) is a factor of the polynomial y= 2x^3 - x^2 - 41x + 70.