Algebra 2 polynomial function question

Question

(Open-Ended) Write a polynomial function in standard form with zeros –5, 3, and 2 ?

Answer 1

Start with

P(x) = (x + 5)(x - 3)(x - 2)

Answer 2

Hi Nicole, this question is asking you to understand what makes polynomial "f(x)" equal zero, and the first part is to write the polynomial as f(x) = (a)(x - ?)(x - ?)(x - ?), then you will have to multiply this all to get to standard form.

The key "clue" is that if you are told a polynomial equals zero when x = 5 and when x = 7, you can write the polynomial as f(x) = a (x - 5)(x - 7) and then multiply to get ax² - 12ax + 35a (where "a" is any number except 0). The complication here is that it would also be true to say f(x) = a(x - 5)²(x - 7)³-- can you see why both answers fit the condition that if you let x = 5 or let x = 7, then you get out zero? In many cases, the problem tells you the degree of the polynomial so there is not more than one correct answer,

Hope this helps, but please let me know--Andrew