Find a polynomial f(x) of degree 3 that has the following zeros. -8,4,0

Answer 1

Any cubic polynomial with three zeros can be written in factored form:

f(x) = a(x − c₁)(x − c₂)(x − c₃)

where a is the leading coefficient and c₁, c₂, and c₃ are the three zeros.

For this problem, the zeros are given as,

c₁ = 0, c₂ = 4, c₃ = -8.

So substituting in these values we have,

f(x) = a*x(x − 4)(x + 8)

Since a can be any real number, there are many different polynomials with those three zeros. We can let a = 1 and get the polynomial,

f(x) = x(x − 4)(x + 8)

By multiplying the factors, we can rewrite this polynomial in standard form as,

f(x) = x³ + 4x² - 32x

Answer 2

f(x) = (x + 8)(x - 4)(x - 0)