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This 8 page Class Notes was uploaded by Gerry Kohler on Sunday October 25, 2015. The Class Notes belongs to MATH 1650 at University of North Texas taught by Jason Snyder in Fall. Since its upload, it has received 47 views. For similar materials see /class/229123/math-1650-university-of-north-texas in Mathematics (M) at University of North Texas.
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Date Created: 10/25/15
Math 1650 Lecture Notes 32 Jason Snyder PhD Dividing Polynomials 32 Dividing Polynomials Long Division of Polynomials I Example 1 I Long Division of Polynomials Divide 6x2 26x 12 by x 4 Division Algorithm IfPx and Dx are polynomials with Dx qt 0 then there exist unique polynomials Qx and Rx where Rx is either 0 or of degree less than the degree of D x such that Px Dx Qx Rx The polynomials Px and Dx are called the dividend and divisor respectively Q x is the quotient and Rx is the remainder Page 1 of 6 Math 1650 Lecture Notes 32 Jason Snyder PhD Dividing Polynomials I Example 2 Long Division of Polynomials I Let Px 8x4 6x2 4x 5 and Dx 4x2 x 2 Find polynomials and Rx such that Px DOC Synthetic Division Synthetic division is a quick way to divide polynomials when the divisor is of the form x C In synthetic division we only write down the essential parts of the long division Page 2 of 6 Math 1650 Lecture Notes 32 Jason Snyder PhD Dividing Polynomials I Example 3 Synthetic Division I Use synthetic division to divide 2x2 7x2 5 by x 3 The Remainder Theorem Remainder Theorem If the polynomial Px is divided by x c then the remainder is the value Pc Proof Page 3 of 6 Math 1650 Lecture Notes 32 Jason Snyder PhD Dividing Polynomials I Example 4 Using the Remainder Theorem to Find the Value of a Polynomial I Let Px 4x5 2x4 3x 5 a Find the quotient and remainder when Px is diVided by X 5 b Use the remainder theorem to nd P 5 Factor Theorem 6 is a zero ofP ifand only ifx c is a factor ofPx Proof Page 4 of 6 Math 1650 Lecture Notes 32 Jason Snyder PhD Dividing Polynomials Exam le 5 Factorin a Pol nomial Usin the Factor Theorem P g y 2 Let Px x3 7x 6 Show that P1 0 and use this fact to factor Px completely I Example 6 I Finding a Polynomial With Speci ed Zeros Find a polynomial of degree 4 that has zeros 3 O and 2 only Homework Due 2 62 even Page 5 of 6 Math 1650 Lecture Notes 32 Jason Snyder PhD Dividing Polynomials Page 6 of 6 Math 1650 Lecture Notes 26 Jason Snyder PhD Modeling with Functions 26 Modeling with Functions Modeling with Functions I Example 1 I Modeling the Volume ofa Box A breakfast cereal company manufactures boxes to package their product For aesthetic reasons the box must have the following proportions Its width is 3 times its depth and its height is 5 times its depth a Find a function that models the volume of the box in terms of its depth b Find the volume of the box if the depth in 15 in c For what depth is the volume 90 m5 d For what depth is the volume greater than 60 in To find the function that models the volume of the box we use the following steps gt Express the Model in Words We know that the volume of a rectangular box is volumezdepth x height gtlt Width gt Choose the Variable There are three varying quantities width depth and height Since the function we want depends on the depth we let x depth ofthe box Then we express the other dimensions of the box in terms of x In words In Algebra Depth x Width 3x Height 5x gt Set up the Model The model is the function V that gives the volume of the box in terms of the depth x volume depth gtlt Width X height Vx x X 3x gtlt 5x Vx 15363 Page 1 of 6
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