Create a polynomial function in factored form that crosses through the x-axis at -2 and touches the x-axis and turns around at 4.​

Given:

A polynomial crosses through the x-axis at -2 and touches the x-axis and turns around at 4.​

To find:

The polynomial function in factored form.

Solution:

If the graph of a polynomial intersect the x-axis at , then is a factor of the polynomial.

If the graph of a polynomial touches the x-axis at , then is a factor of the polynomial with multiplicity 2. In other words is the factor of the polynomial.

It is given that the polynomial crosses through the x-axis at -2. So, is a factor of required polynomial.

It is given that the polynomial touches the x-axis and turns around at 4. So, is a factor of required polynomial.

Now, the required polynomial is:

Therefore, the required polynomial is .