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 the quotient P(x)/D(x) in the form
7. P(x) = 2x4 − x3 + 9x2, D(x) = x2 + 4
Trending nowThis is a popular solution!
Chapter 3 Solutions
Precalculus: Mathematics for Calculus (Standalone Book)
- Stopping 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=40 mph .arrow_forwardUse 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_forwardFuel Efficiency The fuel efficiency (in miles per gallon) of a car going at a speed of x miles per hour is given by the polynomial 1150x2+13x . Find the fuel efficiency when x=30 mph.arrow_forward
- Roller coaster A portion of a roller coasters tracks can be modeled by the polynomial function f(x)=0.0001(x3600x2+90,000x), where 0x400.f(x) represents the height of the roller coaster in feet and x represents the horizontal distance in feet. a. Find the height of the roller coaster when x=100 yards. b. Find the values of x on the interval [0,400] at which the height of the roller coaster is 0 yards.arrow_forwardFill in the blanks. A shortcut method for dividing a polynomial by a binomial of the form xc is called _____ division.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
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
- Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill