Find a polynomial function P(x) with the given zeros. There is no unique answer for
P(x).
−2, 8
P(x) =
If the given zeroes are −2, 8 then
P(x) = (x+2)(x-8)
What "given zeros"?
To find a polynomial function with the given zeros, we can use the fact that if a number is a zero of a polynomial function, then the corresponding linear factor (x - zero) will be a factor of the polynomial.
Since the zeros are -2 and 8, the corresponding linear factors are (x - (-2)) and (x - 8). Simplifying, we get (x + 2) and (x - 8) as the factors.
To find the polynomial function, we multiply these factors together:
P(x) = (x + 2)(x - 8)
Expanding this expression using the distributive property, we get:
P(x) = x(x - 8) + 2(x - 8)
Simplifying further:
P(x) = x^2 - 8x + 2x - 16
Combining like terms:
P(x) = x^2 - 6x - 16
Therefore, a possible polynomial function with the given zeros is P(x) = x^2 - 6x - 16.
To find a polynomial function P(x) with the given zeros, we can use the fact that the zeros of a polynomial function are the values of x for which the function equals zero.
Since the zeros are -2 and 8, we can set up two equations:
(x - (-2)) = 0
(x - 8) = 0
Simplifying these equations, we get:
(x + 2) = 0
(x - 8) = 0
To obtain a polynomial function, we can multiply these factors together:
(x + 2)(x - 8)
Expanding this expression, we get:
x^2 - 6x - 16
Therefore, a polynomial function P(x) with the given zeros of -2 and 8 is:
P(x) = x^2 - 6x - 16