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

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1.

$5x^4+16x^3-15x^2+8x+16;x+4$

Factor ƒ(x) into linear factors given that k is a zero. $\text{ƒ}\left(x\right)=-6x^3-25x^2-3x+4;k=-4$

Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for each given function. f(x)=5x³−3x²+3x−1

Use Descartes' Rule of Signs to explain why $2x^4+6x^2+8=0$ has no real roots.

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. 2x³−x²−9x−4=0

Solve each problem. Give the maximum number of turning points of the graph of each function. ƒ(x)=4x^3-6x^2+2

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. x⁴−3x³−20x²−24x−8=0