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_ x³+ type your answer_ x²+ 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 \(2\), \(0\), and \(4\), the factors are \((x - 2)\), \(x\), and \((x - 4)\).

Step2: Multiply the factors

\[

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

\]

Answer:

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