## heathernelly 3 years ago l

1. CliffSedge

Fundamental theorem of algebra tells you the maximum number of real solutions there are to a polynomial equation. In your example, the highest exponent on x is 5, so there will be at most 5 real solutions.

2. CliffSedge

The other thing to consider is that not only are there a maximum of 5 real solutions, there are guaranteed 5 solutions total (though some of them may be imaginary).

3. heathernelly

how do i solve it though?

4. CliffSedge

If you have multiple choice options, you don't need to solve it. You choose the only one that makes sense. It's a fifth degree polynomial, that means it has 5 roots; which of those options shows 5 roots?

5. heathernelly

ok, bu then then how would that work out for my next equation: x3 – x2 + 5x – 5 = 0

6. CliffSedge

(c) is unclear. What are the solutions there?

7. CliffSedge

(a) and (b) are plausible. The only difference is 1 or -1, so you could test those to see which on is a root.

8. CliffSedge

Ok, well testing x=1 and x=-1 will still narrow it down. If x=1 is a root then it has to be (a). If -1 works, then you can factor it out (use synthetic division or whatever).

9. CliffSedge

Also, this polynomial is factorable, which will show the solutions right away.

10. heathernelly

okay, ty for the help :)

11. CliffSedge

My pleasure.