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DISCUSS: Degrees of Sums and Products of Polynomials Make up several pairs of polynomials, then calculate the sum and product of each pair. On the basis of your experiments and observations, answer the following questions.
(a) How is the degree of the product related to the degrees of the original polynomials?
(b)How is the degree of the sum related to the degrees of the original polynomials?
(c) Test your conclusions by finding the sum and product of the following polynomials:
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Chapter P Solutions
College Algebra
- Fabricating sheet metal The open tray shown in the illustration is to be manufactured from a 12-by-14-inch rectangular sheet of metal by cutting squares from each corner and folding up the sides. If the volume of the tray is to be 160 cubic inches and x is to be an integer, what size squares should be cut from each corner?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_forwardVolume of Concrete A culvert is constructed out of large cylindrical shells cast in concrete, as shown in the figure. Using the formula for the volume of a cylinder given on the inside back cover of this book, explain why the volume of the cylindrical shell is v=R2hr2h Factor to show that v=2averageradiusheightthickness Use the ‘unrolled” diagram to explain why this makes sense geometrically.arrow_forward
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