## mmbuckaroos 3 years ago Use the Factor Theorem to determine a polynomial equation, of lowest degree, that has only the indicated roots: 0 is a root of multiplicity 5, 2 is a double root

1. Mertsj

x^5(x-2)^2=0

2. satellite73

3. mmbuckaroos

so I would get \[x ^{5}+x ^{2}-4x+4\]

4. satellite73

no i don't think so

5. satellite73

\[x^5(x-2)^2=x^5(x-2)(x-2)=...\]

6. mmbuckaroos

where does the extra (x-2)^2 come from then that you have after the x^5?

7. mmbuckaroos

oh nvm.... so what am I multiplying out then? the (x-2)^2 or?

8. Mertsj

\[x^5(x-)(x-2)=x^5(x^2-4x+4)=x^7-4x^6+4x^5\]

9. mmbuckaroos

Oh ok so I just needed to continue multiplying to completly get rid of the parenthisis cool thank you... so what if it is the same question but it says 1/3 is a double root and -2 is a double root? do I set it up like this: f(x)=(x-1/3)^2(x+2)^2

10. Mertsj

Yes

11. mmbuckaroos

awesome thanks so much for the help!

12. Mertsj

yw

13. mmbuckaroos

Uh so I actually have one more silly question how do I get rid of the fraction to make that problem easier?

14. mmbuckaroos

NVM I figured it out:) thanks

15. satellite73

i wouldn't

16. satellite73