Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. x³+2x²+3; x-1

Factor ƒ(x) into linear factors given that k is a zero. $\text{ƒ}\left(x\right)=2x^3-3x^2-5x+6{;}^{}k=1$

Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. n=4; -2, 5, and 3+2i are zeros; f(1) = -96

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for each given function. f(x)=x³+2x²+5x+4

Solve each problem. Is x+1 a factor of ƒ(x)=x³+2x²+3x+2?

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for each given function. $f\left(x\right)=3x^4-2x^3-8x+5$

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