anForm a polynomial f(x) with real coefficients having the given degree and zeros.ResourceDegree 4; zeros: -2+3i; 4 multiplicity 2cible ResourcLet a represent the leading coefficient. The polynomial is f(x) = a(Type an expression using x as the variable. Use integers or fractions for any numbers in the expression. Simplify your an wer.)nunication ToClear allGet more help -Media -TutoringHelp me solve this48°FP Type here to searchF10FBF6미

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Answered: Form a polynomial f(x) with real…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.2: Polynomial Functions Of Higher Degree

Problem 104E: Modeling Polynomials Sketch the graph of a fifth-degree polynomial function that has a zero of...

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(a) Give the general form of polynomial function P of degree n. (b) What does it mean to say that c is a zero of P? Give two equivalent conditions that tell us that c is a zero of P.
Building Envelope The building code in a certain town requires that a house be at least 10 ft from the boundaries of the lot. The buildable area or building envelope for the rectangular lot shown in the following figure is given by A=(x20)(y20) a Explain how the expression for A is obtained. b Expand to express A as a polynomial in x and y. c A contractor has a choice of purchasing one of two rectangular lots, each having the same area. One lot measures 100 ft by 400 ft; the other measures 200 ft by 200 ft. Which lot has the larger building envelope?
Number of Intercepts and Local Extrema How many x-intercepts and how many local extrema does the polynomial P(x)=x34x have? How many x-intercepts and how many local extremadoes the polynomial Q(x)=x3+4x have? If a > 0. bow many x-intercepts and how many local extrema does each Of the polynomials P(x)=x3ax and Q(x)=x3+ax have? Explain your answer.
Too Many Corn Plants per Acre? The more corn a farmer plants per acre, the greater is the yield the farmer can expect. But only up to a point, many plants acre can cause Overcrowding and decrease yields, data give yields per acre for various densities of corn plantings, as found by researchers at a university test farm. (a) Find the quadratic polynormal that best fits the data. (b) Draw a graph of the polynomial from part (a) together with a scatter plot of the data. (c) use your result (b) to estimate the yield for 37000 plants per acre.
Graphing Polynomials Use a graphing device to graphthe polynomial. Find the x- and y-intercept and the coordinateof all local extrema, correct to the nearest decimal. Describe theend behavior of the polynomial. P(x)=x5+x47x3x2+6x+3
Maximize volume An open box is to be constructed from a piece of cardboard 20 inches by 24 inches by cutting a square of length x from each corner and folding up the sides as shown in the figure. a. Write a polynomial function V(x) that expresses the volume of the constructed box as a function of x. b. Use the theory learned about graphing polynomial functions and graph V(x). c. What is the domain of the function as it relates to the application problem? d. Use a graphing calculator to graph the function, and estimate the value of x that gives the maximum volume and then estimate the maximum volume. Round to one decimal place.
Poiseuilles Law for Rate of Fluid Flow Poiseuilles law for the rate of flow of a fluid through a tube is a fourth-order polynomial that is also a power function: F=cR4, where F is the flow rate measured as a volume per unit time, c is a constant, and R is the radius of the tube. a. Assume that R increases by 10. Explain why F increases by 46.41. Hint: Consider 1.10 raised to the fourth power. b. What is the flow rate through a 3/4inch pipe compared with that through a 1/2inch pipe? c. Suppose that an artery supplying blood to the heart muscle see Figure 5.86 is partially blocked and is only half its normal radius. What percentage of the usual blood will flow through the partially blocked artery?
DISCOVER: Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q are the same. P(x)=3x45x3+x23x+5 Q(x)=(((3x5)x+1)x3)x+5 Try to evaluate P(2) and Q(2) in your head, using the forms given. Which is easier? Now write the polynomial R(x)=x52x4+3x32x2+3x+4 in nested form, like the polynomial Q. Use the nested form to find R(3) in your head. Do you see how calculating with the nested form follows the same arithmetic steps as calculating the value of a polynomial using synthetic division?
Local extrema these exercises involve local maximaand minima of polynomial functions. Graph the function P(x)=(x2)(x4)(x5) and determine how many local extrema it has. If a < b < c, explain why the function P(x)=(xa)(xb)(xc) must have two local extrema-
Modeling Polynomials Sketch the graph of a fourth-degree polynomial function that has a zero of multiplicity 2 and a negative leading coefficient. Sketch the graph of another polynomial function with the same characteristics except that the leading coefficient is positive.
Modeling Polynomials Sketch the graph of a fifth-degree polynomial function that has a zero of multiplicity 2and a negative leading coefficient. Sketch the graph of another polynomial function with the same characteristics except that the leading coefficient is positive.

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