Write a polynomial function in standard form with zeros at -3, 2, and -1.

Question

Question: Write a polynomial function in standard form with zeros at -3, 2, and -1.

 

 

Thank you! 

Answer 1

First, we should establish what it means to be a zero. If the function is "zero" at those values, that means that y= 0 at those specific values of x.

 

Think about what a factored function looks like. It usually is something like

 

f(x) = (x-2)(x+3) or something like that.

 

The zeros for the previous function are where (x - 2) = 0 or where (x + 3) = 0. Now we use this general idea with your given zeros.

 

f(x) = (x - 2)(x + 3)(x + 1)

 

To make this function in standard form, we need to multiply it all out. I prefer to work with the two left parts first. FOIL them out to get:

 

f(x) = (x² + 3x - 2x -6)(x +1)

group like terms and we find

f(x) = (x² + x - 6)(x +1)

 

Now multiply those together to get

f(x) = x³ +x² +x² + x - 6x -6

 

Combining like terms again and we find the polynomial in standard form:

 

f(x) = x³ +2x² -5x - 6

 

I hope this helps! Please ask if you have any questions about this problem