# 6.09 Polynomial Functions Research Paper

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6.09 Polynomial Functions Activity Materials Used: box of spaghetti, pencil and paper, Geogebra Procedure: 1. Measure and record the length, width and height of the rectangular box you have chosen. Be sure to use the same measurement for all three dimensions (either centimeters or inches). The rectangular box I chose to measure was a box of spaghetti. The length was 10 inches, the width was 3 inches, and the height was 2 inches. 2. Apply the formula of a rectangular box (V = lwh) to find the volume of the object. Now suppose you knew the volume of this object and the relation of the length to the width and height, but did not know the length. Rewriting the equation with one variable would result in a polynomial equation that you could…show more content…
Simplify the equation and write it in standard form. If the equation contains decimals, multiply each term by a constant that will make all coefficients integers. 60 = (x+0)(x-7)(x-8) f(x) = x^3 - 15x^2 + 56x -60 5. Find the solutions to this equation algebraically using the Fundamental Theorem of Algebra, the Rational Root Theorem, Descartes' Rule of Signs, and the Factor Theorem. Fundamental Theorem of Algebra: The fundamental theorem of algebra states that the number of zeroes is equal to the degree of the polynomial. F(x) = x^3 - 15x^2 + 56x -60 There are three zeroes. Rational Root Theorem: F(x) = x^3 - 15x^2 + 56x -60 In the rational root theorem, the constant term is represented by the letter p, and the leading coefficient is represented by the letter q. In this case, p = +/- 60 and q = +/- 1. Factors of p: ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, ±60 Factors of q: ±1 P/Q simplified: ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±12, ±15, ±20, ±30, ±60 These are the possible zeroes. You can divide the polynomial using these numbers to see if they are a zero of the function. If we use synthetic division, 2 and 3 and 10 are three of the zeroes of the