A polynomial with a n degree has n solutions. The degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients.
A third degree polynomial has 3 solutions. A third degree polynomial, has the following form
[tex]P(x)=ax^3+bx^2+cx+d[/tex]If the third degree polynomial has 3 distinct roots, it can also be written in factorized form, which is
[tex]ax^3+bx^2+cx+d=a(x-x_1)(x-x_2)(x-x_3)[/tex]To find the roots, we just have to find the solutions for the polynomial when it is equal to zero.
[tex]a(x-x_1)(x-x_2)(x-x_3)=0[/tex]If we use 0, 1 and 2 as the solutions for this equation, we have
[tex]\begin{gathered} a(x-0_{})(x-1)(x-2)=0 \\ x(x-1)(x-2)=0 \end{gathered}[/tex]This is an equation with three solutions, and they are 0, 1 and 2.
[tex]x(x-1)(x-2)=0[/tex]
