Expert: Paul Klarreich - 1/23/2008

Question
If a polynomial has root at x=a , then x-a is a factor of the polynomial. Find a 3rd degree polynomial p(x)  with these properties: p(3)=p(-2)=p(0)=0, and p(-1)=4.

Answer
Questioner:   Andrew
Category:  Calculus
Private:  No
 
Subject:  3rd degree polynomial...
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Hi, Andrew,

Question:  If a polynomial has root at x=a , then x-a is a factor of the polynomial.

>> RIGHT!

Find a 3rd degree polynomial p(x)  with these properties:

p(3)= 0  -->  (x - 3) is a factor.
p(-2)= 0 -->  (x + 2) .....
p(0)=0   -->   (x)    .....

So your P(x) = a(x - 3)(x + 2)(x)

But p(-1)=4.

p(-1) = a(-1 - 3)(-1 + 2)(-1)

p(-1) = a(-4)(1)(-1) = 4a = 4, so a = 1, and

So your P(x) = (x - 3)(x + 2)(x), which you can multiply out.