Find a polynomial function of degree 6 with −1 as a zero of multiplicity 3, 0 as a zero of multiplicity 2, and 1 as a zero of multiplicity 1.
The function is f(x) =
follow my steps for you previous like question,
let me know what you got
To find a polynomial function with the given zeros and multiplicities, we can start by writing the factors of the polynomial.
First, we know that -1 is a zero of multiplicity 3. This means that the factor (x - (-1))^3 = (x + 1)^3 appears in the polynomial.
Next, we know that 0 is a zero of multiplicity 2. This means that the factor (x - 0)^2 = x^2 appears in the polynomial.
Finally, we know that 1 is a zero of multiplicity 1. This means that the factor (x - 1)^1 = (x - 1) appears in the polynomial.
Now, we can multiply all the factors together to get the polynomial function:
f(x) = (x + 1)^3 * x^2 * (x - 1)
Expanding this expression will give us the complete polynomial function of degree 6:
f(x) = (x + 1)(x + 1)(x + 1) * x^2 * (x - 1)
Simplifying this expression gives:
f(x) = (x + 1)^3 * x^2 * (x - 1) = (x + 1)(x + 1)(x + 1) * x^2 * (x - 1)
Multiplying this out will give you the final polynomial function.