Question

A polynomial has zeros of -1(mult. 2), 2 and 3

Answer 1

Answer= x^4 - 3x^3 - 3x^2 + 7x +6

1. Write out the 0s
(x + 1)(x + 1)(x - 2)(x - 3)
[[ remember the sign flips ]]

2. Foil the first two.
(x + 1)(x + 1)
x^2 + x + x + 1
x^2 + 2x + 1

3. Foil the second two.
(x - 2)(x - 3)
x^2 - 3x - 2x + 6
x^2 - 5x + 6

4. Foil both polynomials.
(x^2 + 2x + 1) (x^2 - 5x + 6)
..
It comes out as:
x^4 - 3x^3 - 3x^2 + 7x +6
You can check the pic for the work on that.

If you want, check your work by finding the 0s. They should be -1, 2, and 3. Also make sure the highest power is the number of 0s.
The highest power is ^4, and there are 4 zeros (since -1 is mult of 2)