How do i write this equation is factor formed?

Question

1.  zeros: 3, -5; degree: 3; 3 has a multiplicity of 2.
2. zeros: 0, -2, 4; degree: 5; 0 has a multiplicity of 3.
3. zeros: 7/2, -3, 8; degree: 3
4. zeros: -1, 2; degree: 4; -1 has a multiplicity of 3.

Answer 1

For problem 1, if the zeros are 3 and -5, then the factors are (x - 3) and (x + 5). Since 3 has a multiplicity of 2, then the polynomial could be written as (x - 3)²(x + 5) in factored form.

For problem 2, the factors are x - 0 or x, along with (x + 2) and (x - 4).

This fifth-degree polynomial in factored form would be x³(x + 2)(x - 4). The x is cubed because x = 0 has a multiplicity of 3.

Problems 3 and 4 can be handled in the same manner. There is a theorem that states if x = k is a zero of a polynomial, then (x - k) is a factor of the polynomial.