# Factor Theorem and Remainder Theorem

• Sep 8th 2007, 10:22 AM
JonathanEyoon
Factor Theorem and Remainder Theorem
Can anyone explain these to me ? :confused: I'm clueless as to how to do these.

Factor Theorem

Use the Factor Theorem to show that x - c is a factor of P(x) for the given value(s) of c.

P(x) - x^3 - 3x^2 + 3x - 1, c = 1

Also i'm having problems with a type of question that I also don't know where to start.

Find a polynomial of the specified degree that has the given zeros.

Degree 3; Zeros -1 , 1, 3

HELP!!!
• Sep 8th 2007, 10:32 AM
Krizalid
Quote:

Originally Posted by JonathanEyoon
Use the Factor Theorem to show that x - c is a factor of P(x) for the given value(s) of c.

P(x) - x^3 - 3x^2 + 3x - 1, c = 1

Find a polynomial of the specified degree that has the given zeros.

Degree 3; Zeros -1 , 1, 3

\$\displaystyle x-1\$ will be a factor of \$\displaystyle P(x)\$ if \$\displaystyle P(1)=0\$, i.e. \$\displaystyle P(1)=1^3-3(1)^2+3(1)-1=0\$

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Given the zeros, you can set \$\displaystyle (x+1)(x-1)(x-3)=0\$, now expand.
• Sep 8th 2007, 10:50 AM
JonathanEyoon
Quote:

Originally Posted by Krizalid
\$\displaystyle x-1\$ will be a factor of \$\displaystyle P(x)\$ if \$\displaystyle P(1)=0\$, i.e. \$\displaystyle P(1)=1^3-3(1)^2+3(1)-1=0\$

_____

Given the zeros, you can set \$\displaystyle (x+1)(x-1)(x-3)=0\$, now expand.

Ohhhhhhhhh ok.... so what does the factor theorem and remainder theorem mean?