Question

What is the standard form for yt and factored form

Answer 1

Given:

The leading coefficient of a polynomial is 3.

And the roots of the polynomial is -1, 1, and 2.

Required:

To write g(t) in factored form and standard form.

Step-by-step explanation:

From the given data, the factored form is given by

`\begin{gathered} g(t)=3(x-(-1))(x-1)(x-2) \\ =3(x+1)(x-1)(x-2) \end{gathered}`

The standard form is,

`\begin{gathered} g(t)=3(x+1)(x^2-2x-x+2) \\ =3(x+1)(x^2-3x+2) \\ =3(x^3-3x^2+2x+x^2-3x+2) \\ =3(x^3-2x^2-x+2) \\ =3x^3-6x^2-3x+6 \end{gathered}`

Final Answer:

The factored form:

`g(t)=3(x+1)(x-1)(x-2)`

The standard form:

`g(t)=3x^3-6x^2-3x+6`