Question

A polynomial function with a leading coefficient of 1 and multiplicity 1 for each root has the following factors

Answer 1

2 and 4

Explanation:

Answer 2

`(x-2)\cdot(x-(1+\sqrt[]{5}))\cdot(x+\sqrt[]{3})`

If one choose the first factor (which is the conjugated binomial of x-2) and add it to our polinomial we would have:

`\begin{gathered} (x+2)\cdot(x-2)\cdot(x-(1+\sqrt[]{5}))\cdot(x+\sqrt[]{3}) \\ (x-2)^2\cdot(x-(1+\sqrt[]{5}))\cdot(x+\sqrt[]{3}) \end{gathered}`

This means, for the first factor, 2 is a root of multiplicity 2.

The sentence specify that the polinomial has multiplicity of 1 for each root, therefore, we cannot use either the conjugated binomial or the square binomial of the roots.

Thus, the only factor which is not changing the multiplicity is:

`x+(1-\sqrt[]{3})`