Question

Please Help!!!

Answer 1

Answer:

$p(x) = {x}^{4} + {x}^{3} - 7 {x}^{2} - x + 6$

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

$p(x) = (x - 1)(x + 1)(x + 3)(x - 2)$

We expand to get:

$p(x) = ( {x}^{2} - 1)( {x}^{2} + x - 6)$

We expand further to get:

$p(x) = {x}^{2}( {x}^{2} + x - 6) - 1({x}^{2} + x - 6)$

$p(x) = {x}^{4} + {x}^{3} - 6 {x}^{2} - {x}^{2} - x + 6$

This simplifies to:

$p(x) = {x}^{4} + {x}^{3} - 7 {x}^{2} - x + 6$

This is the standard form of the polynomial since it is written in descending powers of x.