Question

How do you write a polynomial function of least degree with integral coefficients that has the given zeros 3, 1, -2, -4?

Answer 1

`color(green)(x^4+2x^3-13x^2-14x+24)`

Explanation:

If the polynomial has zeros at
`color(white)("XXX")color(red)(3), color(blue)(1), color(magenta)(-2),color(orange)(-4)`
then it has factors
`color(white)("XXX")(x-color(red)(3)), (x-color(blue)1), (x-color(magneta)(""(-2))), (x-color(orange)(""(-4)))`

`(x-3) * (x-1) * (x+2) * (x+4)`

`color(white)("XXXXXXXXX")=x^4+2x^3-13x^2-14x+24`