BackIn 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.
Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function.
Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function.
In Exercises 51–54, graphs of fifth-degree polynomial functions are shown. In each case, specify the number of real zeros and the number of imaginary zeros. Indicate whether there are any real zeros with multiplicity other than 1.
Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function.
Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=4x^3-37x^2+50x+60 Find the zero in part (b) to three decimal places.
For each polynomial function, find all zeros and their multiplicities.
Factor ƒ(x) into linear factors given that k is a zero.
Show that each polynomial function has a real zero as described in parts (a) and (b). In Exercises 31 and 32, also work part (c). ƒ(x)=3x^3-8x^2+x+2 Find the zero in part (b) to three decimal places.
Exercises 53–60 show incomplete graphs of given polynomial functions. a) Find all the zeros of each function. b) Without using a graphing utility, draw a complete graph of the function. f(x)=2x4−3x3−7x2−8x+6
Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. 4x2+2x+54; x-4
Determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of each function.
Find all zeros of f(x) = x³ + 5x² – 8x + 2.
In Exercises 1–8, use the Rational Zero Theorem to list all possible rational zeros for each given function. f(x)=3x4−11x3−3x2−6x+8