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.
Explanation:
From the given data, the factored form is given by
[tex]\begin{gathered} g(t)=3(x-(-1))(x-1)(x-2) \\ =3(x+1)(x-1)(x-2) \end{gathered}[/tex]
The standard form is,
[tex]\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}[/tex]
Final Answer:
The factored form:
[tex]g(t)=3(x+1)(x-1)(x-2)[/tex]
The standard form:
[tex]g(t)=3x^3-6x^2-3x+6[/tex]
