Write a polynomial function in standard form with the given zeros: x=2,-2,4
f(x) = (x-2)(x+2)(x-4)
or
f(x) = a(x-2)(x+2)(x-4) , where a is a constant
expand if needed
To find a polynomial function with the given zeros, we can use the zero-factor property. The zero-factor property states that if a polynomial function has a zero at x = a, then the corresponding factor is (x - a).
In this case, the zeros are x = 2, x = -2, and x = 4.
To find the polynomial function, we can multiply these factors together:
(x - 2)(x + 2)(x - 4)
Multiplying this out gives:
(x - 2)(x + 2)(x - 4) = (x^2 - 4)(x - 4)
= (x^2 - 4x - 4x + 16)
= (x^2 - 8x + 16)
So, the polynomial function in standard form with the given zeros is:
f(x) = x^2 - 8x + 16
To write a polynomial function in standard form with the given zeros, we can use the factored form of a polynomial. The factored form looks like this:
f(x) = a(x - r1)(x - r2)(x - r3)...
Where "a" is the leading coefficient and "r1", "r2", "r3", etc. are the zeros of the polynomial.
Therefore, with the zeros x = 2, x = -2, and x = 4, the factored form of the polynomial is:
f(x) = a(x - 2)(x + 2)(x - 4)
To find the value of "a" in the polynomial, we need additional information. For example, if you know a point on the graph of the polynomial (such as the y-intercept), you can substitute that point into the equation and solve for "a". Without this information, we cannot determine the exact value of "a".
So, the polynomial in standard form with the given zeros would be:
f(x) = a(x - 2)(x + 2)(x - 4)