Concept explainers
Division of Polynomials Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(x), and express P in the form
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
College Algebra
- Use synthetic division to show that x=3 is a zero of the function f(x)=2x35x26x+15. Use the result to factor the polynomial function completely and list all the zeros of the function.arrow_forwardRemainder Theorem Let P(x)=6x740x6+16x5200x460x369x2+13x139 Calculate P(7) by (a) using synthetic division and (b) substituting x=7 into the polynomial and evaluating directly.arrow_forwardDISCOVER: 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?arrow_forward
- Use the Remainder Theorem to find the remainder when f(x)=x37x+12 is divided by x+3 .arrow_forwardUsing Descartes’ Rule of Signs. we can tell that the polynomial P(x)=x53x4+x2+8x8 has _______________, ____________________positive real zeros and _____________negative real zeros.arrow_forwardBuilding 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?arrow_forward
- Fill in the blanks. A shortcut method for dividing a polynomial by a binomial of the form xc is called _____ division.arrow_forwardStopping Distance The number of feet it takes for a car traveling at x miles per hour to stop on dry, level concrete is given by the polynomial 0.06x2+ 1. 1x. Find the stopping distance when x = 60 mph.arrow_forwardIf we divide the polynomial P by the factor xc and we obtain the equation P(x)=(xc)Q(x)+R(x), then we say that xc is the divisor, Q(x) is the _________, and R(x) is the ________.arrow_forward
- 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.arrow_forwardThe polynomial 6x2+15xy gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side x feet and sides of height y feet. Find the cost of producing a box with x=5 feet and y=8 feet.arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt