Answer:
[tex]P(x)=x^3+x^2[/tex]
Step-by-step explanation:
Polynomials
Given the roots or zeros of a polynomial as x1, x2, x3, ...xn and the leading factor a, the polynomial can be expressed as:
[tex]P(x)=a(x-x_1)(x-x_2)(x-x_3)...(x-x_n)[/tex]
We are given the zeros of a polynomial as x1=0, x2=0 (multiplicity or zeros), and x3=-1, thus the polynomial is:
[tex]P(x)=a(x-0)(x-0)(x+1)[/tex]
Operating:
[tex]P(x)=a.x.x(x+1)[/tex]
[tex]P(x)=ax^2(x+1)[/tex]
[tex]P(x)=ax^3+ax^2[/tex]
Assuming a=1, the polynomial is
[tex]\mathbf{P(x)=x^3+x^2}[/tex]
