Question

writing equations cw/hw
write a polynomial function of least degree with integral coefficients that has the given zeros. the last question will require you to upload a picture of your work.
1 fill in the blank 1 point
2, 0, 4
f(x) = type your answer... x^3+ type your answer... x^2+ type your answer... x

Explanation:

Step1: Use zero - factor form

If \(x = a\) is a zero of a polynomial, then \((x - a)\) is a factor. Given zeros \(x = 2\), \(x=0\), and \(x = 4\), the factors are \((x - 2)\), \(x\), and \((x - 4)\).

Step2: Multiply the factors

\[

$$\begin{align*} f(x)&=x(x - 2)(x - 4)\\ &=x(x^{2}-4x-2x + 8)\\ &=x(x^{2}-6x + 8)\\ &=x^{3}-6x^{2}+8x \end{align*}$$

\]

Answer:

1. \(1\)
2. \(-6\)
3. \(8\)