Answer:
[tex]p(x) = {x}^{4} + {x}^{3} - 7 {x}^{2} - x + 6[/tex]
Step-by-step explanation:
The polynomial function has zeros
x=1, x=2,x=-3,x=-1
This means the factored form of the polynomial is
[tex]p(x) = (x - 1)(x + 1)(x + 3)(x - 2)[/tex]
We expand to get:
[tex]p(x) = ( {x}^{2} - 1)( {x}^{2} + x - 6)[/tex]
We expand further to get:
[tex]p(x) = {x}^{2}( {x}^{2} + x - 6) - 1({x}^{2} + x - 6)[/tex]
[tex]p(x) = {x}^{4} + {x}^{3} - 6 {x}^{2} - {x}^{2} - x + 6[/tex]
This simplifies to:
[tex]p(x) = {x}^{4} + {x}^{3} - 7 {x}^{2} - x + 6[/tex]
This is the standard form of the polynomial since it is written in descending powers of x.
