Solve each problem. Find a polynomial function ƒ of degree 3 with -2, 1, and 4 as zeros, and ƒ(2)=16.

In Exercises 33–38, use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for each given function. f(x)=x^3+2x^2+5x+4

For each polynomial function, one zero is given. Find all other zeros. See Examples 2 and 6. ƒ(x)=x^3+4x^2-5; 1

Solve each problem. Is x+1 a factor of ƒ(x)=x^3+2x^2+3x+2?

In Exercises 37–38, use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for each given function. f(x) = 3x^4 - 2x^3 - 8x + 5

In Exercises 49–50, find all the zeros of each polynomial function and write the polynomial as a product of linear factors. g(x) = x^4 - 6x^3 + x^2 + 24x + 16

For each polynomial function, find all zeros and their multiplicities. ƒ(x)=5x^2(x^2-16)(x+5)

In Exercises 39–52, find all zeros of the polynomial function or solve the given polynomial equation. Use the Rational Zero Theorem, Descartes's Rule of Signs, and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first zero or the first root. 2x^5+7x^4−18x^2−8x+8=0

Find a polynomial function ƒ(x) of least degree having only real coefficients and zeros as given. Assume multiplicity 1 unless otherwise stated. See Examples 4–6.2-i, 3, and -1