Question

Write a polynomial function in standard form for the given set of roots.

Answer 1

Answer:

$f(x) = {x}^{4} +4 {x}^{3} + 3 {x}^{2}$

Step-by-step explanation:

Let f(x) be the polynomial.

If x=-3, x=0,x=0, x=1 are roots ,then by the factor theorem, x+3=0,x=0,x=0, x+1=0 are factors of f(x).

This implies that:

$f(x) = (x + 3)(x)(x)(x + 1)$

$f(x) = {x}^{2} ( {x}^{2} + x + + 3x + 3)$

$f(x) = {x}^{2} ( {x}^{2} +4x + 3)$

Expand further to get:

$f(x) = {x}^{4} +4 {x}^{3} + 3 {x}^{2}$