Exercises 82–84 will help you prepare for the material covered in the next section. Solve: x²+4x−1=0

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. f(x)=3x⁴−11x³−x²+19x+6

In Exercises 49–50, find all the zeros of each polynomial function and write the polynomial as a product of linear factors. $f\left(x\right)=2x^4+3x^3+3x-2$

For each polynomial function, find all zeros and their multiplicities. $\text{ƒ}\left(x\right)=3x(x-2)(x+3)(x^2-1)$

Find a polynomial function ƒ(x) of least degree having only real coefficients and zeros as given. Assume multiplicity 1 unless otherwise stated. 5+i and 5-i

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

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

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. See Example 7. ƒ(x)=9x⁶-7x⁴+8x²+x+6

Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function. $\text{ƒ}\left(x\right)=7x^5+6x^4+2x^3+9x^2+x+5$