Form a polynomial whose zeros and degree are given.
Zeros: 4 , multiplicity $1 ; \quad-3$, multiplicity 2 ; degree 3
Answer
Final Answer: The polynomial whose zeros are 4 with multiplicity 1 and -3 with multiplicity 2 and degree 3 is \(\boxed{x^3 + 2x^2 - 15x - 36}\).
Step 1 ：The zeros of a polynomial are the values for which the polynomial equals zero. If a polynomial has a zero of multiplicity n, it means that the factor corresponding to that zero appears n times.
Step 2 ：The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the degree is 3, which means the polynomial will have 3 factors.
Step 3 ：The zeros are 4 with multiplicity 1 and -3 with multiplicity 2. This means that the factors of the polynomial will be \((x-4)\) and \((x+3)^2\).
Step 4 ：By expanding these factors, we get the polynomial \(x^3 + 2x^2 - 15x - 36\).
Step 5 ：Final Answer: The polynomial whose zeros are 4 with multiplicity 1 and -3 with multiplicity 2 and degree 3 is \(\boxed{x^3 + 2x^2 - 15x - 36}\).
