Problem

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)= (Simplify your answer. )

Answer

Expert–verified
Hide Steps
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 x(x5)(x+2).

Steps

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 (xzero). In this case, the zeros are -2, 0, and 5. So, the polynomial can be formed by multiplying the factors (x(2)), (x0), and (x5).

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(x5)(x+2).

Step 4 :Simplifying this expression, we get the same polynomial x(x5)(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 x(x5)(x+2).

link_gpt