1. Determine the end behavior, plot the y-intercept, find and plot all real zeros, and plot at least one test value between each intercept. Then connect the points with a smooth curve. f(x)=−x3−11x2−24x+36 Choose the correct end behavior for f(x). The ends of the graph will extend in the same direction, because the degree of the polynomial is even. The ends of the graph will extend in the same direction, because the degree of the polynomial is odd. The ends of the graph will extend in opposite directions, because the degree of the polynomial is odd.
1. Determine the end behavior, plot the y-intercept, find and plot all real zeros, and plot at least one test value between each intercept. Then connect the points with a smooth curve. f(x)=−x3−11x2−24x+36 Choose the correct end behavior for f(x). The ends of the graph will extend in the same direction, because the degree of the polynomial is even. The ends of the graph will extend in the same direction, because the degree of the polynomial is odd. The ends of the graph will extend in opposite directions, because the degree of the polynomial is odd.
1. Determine the end behavior, plot the y-intercept, find and plot all real zeros, and plot at least one test value between each intercept. Then connect the points with a smooth curve. f(x)=−x3−11x2−24x+36 Choose the correct end behavior for f(x). The ends of the graph will extend in the same direction, because the degree of the polynomial is even. The ends of the graph will extend in the same direction, because the degree of the polynomial is odd. The ends of the graph will extend in opposite directions, because the degree of the polynomial is odd.
1. Determine the end behavior, plot the y-intercept, find and plot all real zeros, and plot at least one test value between each intercept. Then connect the points with a smooth curve.
f(x)=−x3−11x2−24x+36
Choose the correct end behavior for f(x).
The ends of the graph will extend in the same direction, because the degree of the polynomial is even.
The ends of the graph will extend in the same direction, because the degree of the polynomial is odd.
The ends of the graph will extend in opposite directions, because the degree of the polynomial is odd.
The ends of the graph will extend in opposite directions, because the degree of the polynomial is even.
2.Use the rational zeros theorem to determine the potential rational zeros of the polynomial function. Do not find the zeros.
f(x)=2x3−27x6+11x2+16−7x
List the potential rational zeros of the polynomial function.
(Type an integer or a fraction. Use a comma to separate answers as needed.)
3.Determine the possible number of positive real zeros and negative real zeros of each polynomial function using Descartes' rule of signs.
f(x)=−3x5+11x4−16x3+7x2−9x+12
The possible number of positive real zeros is
(Type a whole number. Use a comma to separate answers as needed.)
4.Determine the possible number of positive real zeros and negative real zeros of each polynomial function using Descarates' rule of signs.
f(x)=−8x4+7x3−4x2+7x−13
The possible number of positive real zeros is?
(Type a whole number. Use a comma to separate answers as needed.)
5.Find all complex zeros of the given polynomial function, and write the polynomial in completely factored form.
f(x)=4x3−5x2−23x+6
Find the complex zeros of f. Repeat any zeros if their multiplicity is greater than 1.
x=?
(Simplify your answer. Use a comma to separate answers as needed. Express complex numbers in terms of
i.
Use integers or fractions for any numbers in the expression.)
6.Find all complex zeros of the given polynomial function, and write the polynomial in completely factored form.
f(x)=2x3+5x2−22x−55
Find the complex zeros of f. Repeat any zeros if their multiplicity is greater than 1.
x=?
(Simplify your answer. Use a comma to separate answers as needed. Express complex numbers in terms of
i.
Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)
7.Find all complex zeros of the given polynomial function, and write the polynomial in completely factored form.
f(x)=−2x3−11x2−62x+34
Find the complex zeros of f. Repeat any zeros if their multiplicity is greater than 1.
x=?
(Simplify your answer. Use a comma to separate answers as needed. Express complex numbers in terms of
i.
Use integers or fractions for any numbers in the expression.)
8.Find all complex zeros of the given polynomial function, and write the polynomial in completely factored form.
f(x)=2x4−11x3+20x2−7x−10
Find the complex zeros of f. Repeat any zeros if their multiplicity is greater than 1.
x=?
(Simplify your answer. Use a comma to separate answers as needed. Express complex numbers in terms of
i.
Use integers or fractions for any numbers in the expression.)
9.Solve the polynomial equation in the complex numbers.
x3+7x2+7x−15=0
x=?
(Type an exact answer, using radicals as needed. Express complex numbers in terms of
i.
Use a comma to separate answers as needed.)
10.Solve the polynomial equation in the complex numbers.
x4+6x3+6x2+6x+5=0
The solution set is ?
(Type an exact answer, using radicals as needed. Express complex numbers in terms of
i.
Use a comma to separate answers as needed.)
Combination of a real number and an imaginary number. They are numbers of the form a + b , where a and b are real numbers and i is an imaginary unit. Complex numbers are an extended idea of one-dimensional number line to two-dimensional complex plane.
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