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Division of Polynomials Two polynomials P and D aregiven. Use either synthetic or long division to divide P(x) by D(x), and express the quotient P(x)/D(x) in the form
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College Algebra
- Using Descartes’ Rule of Signs. we can tell that the polynomial P(x)=x53x4+x2+8x8 has _______________, ____________________positive real zeros and _____________negative real zeros.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_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_forward
- 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?arrow_forwardNumber 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 P(x)=5x2(x4)3(x+7) has degree ___________. It has zeros 0, 4, and ______________. The zero has multiplicity _________arrow_forward
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