if a polynomial of a function has the x-intercepts of 0, −2, 1, and 7, which expression can represent this function?
To represent a polynomial function with the given x-intercepts, we can use the factored form of the polynomial
To represent a polynomial function with the given x-intercepts, we can use the factored form of the polynomial.
Since the x-intercepts are 0, -2, 1, and 7, we know that the factors of the polynomial would be (x – 0), (x – (-2)), (x – 1), and (x – 7).
Simplifying these factors, we get (x), (x + 2), (x – 1), and (x – 7).
To find the expression that represents the function, we multiply these factors together:
(x)(x + 2)(x – 1)(x – 7)
Expanding this expression, we get:
x(x^3 – 7x^2 + 2x – 14)
Which simplifies to:
x^4 – 7x^3 + 2x^2 – 14x
Therefore, the expression that represents the function with x-intercepts of 0, -2, 1, and 7 is:
f(x) = x^4 – 7x^3 + 2x^2 – 14x.
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