Answer:
[tex]P(x) = 2x^3 - 8x^2 + 6x[/tex]
Step-by-step explanation:
Given
[tex]p =2[/tex] -- Leading coefficient
[tex]Zeros: 0, 1\ and\ 3[/tex]
Required
Determine the polynomial
Represent the zeros with a, b and c.
Such that
[tex]a = 0[/tex]
[tex]b = 1[/tex]
[tex]c = 3[/tex]
The polynomial is:
[tex]P(x) = p * (x - a) * (x - b) * (x - c)[/tex]
[tex]P(x) = 2 * (x - 0) * (x - 1) * (x - 3)[/tex]
[tex]P(x) = 2x * (x - 1) * (x - 3)[/tex]
Open bracket
[tex]P(x) = (2x^2 - 2x) * (x - 3)[/tex]
[tex]P(x) = 2x^3 - 6x^2 - 2x^2 + 6x[/tex]
[tex]P(x) = 2x^3 - 8x^2 + 6x[/tex]
