how do you write the simplest polynomial function with the given zeros
if the given zeros are a,b,c,... then the polynomial is
y = (x-a)(x-b)(x-c)...
To write the simplest polynomial function with the given zeros, follow these steps:
1. Identify the given zeros: Zeros are the values of x where the polynomial function equals zero. For example, let's say the given zeros are x = a, x = b, and x = c.
2. Write the factors: For each given zero, write a factor of the form (x - zero). In our example, we would have (x - a), (x - b), and (x - c).
3. Multiply the factors: Multiply all the factors together. In our example, the polynomial function would be (x - a)(x - b)(x - c).
4. Optionally, simplify the polynomial: If you need to simplify the polynomial, you can expand it. For instance, if you expand (x - a)(x - b)(x - c), you would have x^3 - (a + b + c)x^2 + (ab + ac + bc)x - abc.
So, the simplest polynomial function with the given zeros is (x - a)(x - b)(x - c).