Form a polynomial whose real zeros and degree are given.
Zeros: $-2,0,5$; degree: 3
Type a polynomial with integer coefficients and a leading coefficient of 1.
$f(x)=\square$ (Simplify your answer. $)$
Answer
Final Answer: The polynomial with integer coefficients and a leading coefficient of 1, whose real zeros are -2, 0, and 5, and degree is 3, is \(\boxed{x(x - 5)(x + 2)}\).
Step 1 ：The zeros of a polynomial are the values of x for which the polynomial equals zero. If we know the zeros of a polynomial, we can form the polynomial by multiplying factors of the form \((x - zero)\). In this case, the zeros are -2, 0, and 5. So, the polynomial can be formed by multiplying the factors \((x - (-2))\), \((x - 0)\), and \((x - 5)\).
Step 2 ：The degree of the polynomial is the highest power of x in the polynomial. Since the degree is 3, and we have 3 factors, each of degree 1, we don't need to add any more factors.
Step 3 ：Thus, the polynomial is \(x*(x - 5)*(x + 2)\).
Step 4 ：Simplifying this expression, we get the same polynomial \(x*(x - 5)*(x + 2)\).
Step 5 ：Final Answer: The polynomial with integer coefficients and a leading coefficient of 1, whose real zeros are -2, 0, and 5, and degree is 3, is \(\boxed{x(x - 5)(x + 2)}\).
