Answer:
[tex]f(x) = {x}^{3} + 3 {x}^{2} - x -3[/tex]
Step-by-step explanation:
The given polynomial has zeros at:
x=−3, x=−1, and x=1.
This means that:
x+3, x+1, and x-1 are all factors of this polynomial.
The factored form of this polynomial is :
[tex]f(x) = (x + 3)(x + 1)(x - 1)[/tex]
We expand the last two factors using difference of two squares.
[tex]f(x) = (x + 3)( {x}^{2} - 1)[/tex]
[tex]f(x) = x ( {x}^{2} - 1) + 3( {x}^{2} - 1)[/tex]
[tex]f(x) = {x}^{3} - x+ 3 {x}^{2} -3[/tex]
[tex]f(x) = {x}^{3} + 3 {x}^{2} - x -3[/tex]
This is the standard form because it is now in decreasing powers of x.
