Expert: Steve Holleran - 2/27/2007

Question
apolynomial in x has degree 3 and has roots at x=2, x=-3 and x=3. the value
of the polynomial is 56 when x =4. Find the polynomial in form

k(x-b)(x-c)(x-d)


Answer
Hi Pearl,

This is not as difficult as you might think.

Any time you know the roots of a polynomial, you then know its factors:

If x=2 is a root, then (x-2) is a factor.
If x=3 is a root, then (x-3) is a factor.
If x= -3 is a root, then (x-(-3))=(x+3) is a factor.

so now you can write P(x) as

P(x) = k * (x-2)(x-3)(x+3)

If we find P(4), it has to equal 56:

P(4) = k * (4-2)(4-3)(4+3) = 56

    = k * 2 * 1 * 7  = 56

       k * 14 = 56   so k = 4 , which now gives you:

P(x) = 4 ( x-2) ( x-3) ( x+3) .

I hope this was ok and helps you out.

Steve Holleran