Thread: Contructing Polynomial Functions

I have to make a polynomial function that uses these:

Third-degree, with zeros of -3, -1, and 2, and passes through the point (4, 7)

Hello !

Originally Posted by mankvill

I have to make a polynomial function that uses these:

Third-degree, with zeros of -3, -1, and 2, and passes through the point (4, 7)

If -3, -1 and 2 are zeros of the polynomial P(x), then x-(-3)=x+3, x+1 and x-2 divide P(x).

But (x+3)(x+1)(x-2) is already a polynomial of degree 3. So P(x) is just proportional to (x+3)(x+1)(x-2).



But we know that . Substituting, you can get a

...I'm confused. What is the answer, then?

Originally Posted by mankvill

...I'm confused. What is the answer, then?

Because (4,7) belongs to the polynomial function,


---->




Develop to get the complete polynomial

Is this correct?

edit: i don't know how to make a nominator and denominator, obviously

Originally Posted by mankvill

Is this correct?

Yes
And when checking, we get P(-3)=P(-1)=P(2)=0 and P(4)=7, which is exactly what we wanted

edit: i don't know how to make a nominator and denominator, obviously

\frac{numerator}{denominator}