Answer:
[tex]f(x)=x^{4}+x^{3}-7x^{2}-x+6[/tex]
Step-by-step explanation:
The zeros of the polynomial are: -3, -1, 1, 2
According to the factor theorem, the factors of the polynomial will be:
(x - (-3)) = x + 3
(x - (-1)) = x + 1
(x - 1)
(x - 2)
Since we have the factors, we can multiply them to obtain the equation of the polynomial.
So,
[tex]f(x)=(x+3)(x+1)(x-1)(x-2)\\\\ f(x)=(x+3)(x^{2}-1)(x-2)\\\\ f(x)=(x^{2}-1)(x^{2}-2x+3x-6)\\\\ f(x)=(x^{2}-1)(x^{2}+x-6)\\\\ f(x)=x^{4}+x^{3}-6x^{2}-x^{2}-x+6\\\\ f(x)=x^{4}+x^{3}-7x^{2}-x+6[/tex]
The above equation give the polynomial with integer coefficients and a leading coefficient of 1
