Question

For x = 5, 6, 7, write a polynomial function in standard form with the given zeros.

Answer 1

A polynomial function with given zeros x=5, 6, 7 is found by multiplying the factors (x - 5), (x - 6), and (x - 7) together and expanding them to get the polynomial in standard form, which is x³ - 18x² + 107x - 210.

Step-by-step explanation:

To write a polynomial function with given zeros of x = 5, 6, 7, we use the fact that if a polynomial has zeros at these points, then (x - 5), (x - 6), and (x - 7) are factors of the polynomial.

Step-by-step explanation:

1. Write the factors corresponding to each zero: (x - 5), (x - 6), (x - 7).
2. Multiply the factors together: (x - 5)(x - 6)(x - 7).
3. Expand the product to get the polynomial in standard form, which should be: x³ - 18x² + 107x - 210.

This polynomial is now in standard form with the given zeros.