Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $\text{ƒ}\left(x\right)=5x^6-6x^5+7x^3-4x^2+x+2$

Find all complex zeros of each polynomial function. Give exact values. List multiple zeros as necessary. $\text{ƒ}\left(x\right)=x^4+x^3-9x^2+11x-4$

Solve: $x^4-6x^3+4x^2+15x+4=0$.

Use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x)=x³+x²−4x−4

In Exercises 9–16, a) List all possible rational zeros. b) Use synthetic division to test the possible rational zeros and find an actual zero. c) Use the quotient from part (b) to find the remaining zeros of the polynomial function. f(x)=x³+x²−4x−4

In Exercises 9–16, a) List all possible rational zeros. b) Use synthetic division to test the possible rational zeros and find an actual zero. c) Use the quotient from part (b) to find the remaining zeros of the polynomial function. f(x)=x³−2x²−11x+12

In Exercises 9–16, a) List all possible rational zeros. b) Use synthetic division to test the possible rational zeros and find an actual zero. c) Use the quotient from part (b) to find the remaining zeros of the polynomial function. f(x)=2x³+x²−3x+1

Find the zeros for each polynomial function and give the multiplicity of each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. $f\left(x\right)=-2(x-1)(x+2{)}^2(x+5{)}^3$