Question

Write a polynomial function in standard form with zeros at −3, −1, and 1.

Answer 1

Answer:

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

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 :

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

We expand the last two factors using difference of two squares.

$f(x) = (x + 3)( {x}^{2} - 1)$

$f(x) = x ( {x}^{2} - 1) + 3( {x}^{2} - 1)$

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

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

This is the standard form because it is now in decreasing powers of x.