IM Alg2.2.15 Lesson: The Remainder Theorem

What do you notice? What do you wonder?
[table][tr][td][img]data:image/png;base64,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[/img][/td][td][img]data:image/png;base64,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[/img][/td][td][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEcAAACUCAYAAADBGjSeAAAI90lEQVR4Ae2dz3EUOxCHnQHOADKwM4AMIAPjCOwLZ8gAAqAKHIHJwM7AVb5wgwSo4sxpXn1b78dr+kk9f1a7q1m6q6Y0knq00jetHqln1z4ZUqoETqo1WTEknMAIEk7CCQgEVWk5a4Xz/fv34d27d8OLFy82B3kvU3T8NVPz3VrOp0+fhpOTk+Hi4mJ4//795vBwrM7bt2+LOlNBlPS6hHN3d7cBQ1qTh4eHjQ6AdiVdwnn58uXGYqJBY1Ecu5Qu4TCdbm9vN+PGerASL0+fPh1kNTUdf83cfHdwNF2urq4GADx//nx48uTJcH5+/gckAOKLTk9Pf+s8e/bsD525MLx+d3Dkb87OzoafP3/+7i9TjacWQjlwvA7TDECtpDs4shw/lQRNA7dTT2U8zSj3TzXVz027g8MAGKCHI2gaODoA81Ir93pT8l3Cwc+wbrGC88X3SJhC+CUrOHHgtJJ2LbXq0TBsLIJBfvjwYWNBX7582TheC0zTzOrgbzywbbrVJRwGhBXgcIFEypPJC4Ckw5PNwvO6S/LdwlkymNbXJJyAaMJJOAGBoKqJ5Xz9+nXo7fj161cw7GlVTeB8/PhxuLy8HEh7ObqBw31g5dpyjTHt3u5Wq4nlqIusRUpLetWvLW0Kh90yi7JjkaZwgMKeR0GotUMK4TBNiP7bY2zgLPuJvdQE38R+iNjMq1evNm3buA3XkUeHevT4fO3Gbbvs1F+/fr3RIS3pWP255yEc7WvYJesYc7p0sLYzVh3w2Adx0C7RPAFCh913SceGMTjnOumRkm8JaBTOEgcLnFonS+V+01jSwZfZjSUwOKwAumXQvQqHO1mzANuh0jkDmQPVD7zUJgO3VkvfFISXPlMe62klVTgMbikcBjIVjgJUkb6igNLxecFQn0uWJ505aRWOOgAgHThHyscEOP6u2mu4wzhQ3ijUdKXDZ2JZtj1BsG1yrj4Loq+fm6/CoSF7BzhnPk9xemOWw8DxH0wT/A0A5JA1gJKObkwNDn3kRu4FjjpqU54kpaic15nTQWB652rb45x6ICKC44GqXBB9G3PzoeWUGmMg9qlR0uHu+Y6X9FRGe2OOFEuiXUnJQuS/pLNt+t+nTWhJTzA7//1l3D18xBxhegE9EnRsu+jbpxfXMu3HLDD6DF9XhcOd+vz583B/f//7DYAcqG/E5plyvtOqp01WvmqTlNUvViDg6FxfX2908CHAlg51Ek0htUdq25HeNmkVDh/O3cHH8KFai4xNF/SsI7edo03urNrEGZOnXOJ1tFq2OtIFKG3QP1IBVv22aRXOkoZxhC1XqEv60PKapnCwgjHLatn5XbfVDA7+oNUjdNeDntp+Mzg1PzO1Iz3qNYPT4+C27VPCCQgmnIQTEAiq0nISTkAgqDqI5bDM1xsN9m8lYTHJfgm9qTqtF6B7hcMika+msQ9im8HB3okNrR0YeoQw2Kehg77XQX9MpwR9Ttle4dAxvzlkkACyATS2IRwSdABk40hAA56gkmpzrOu2TfcOp9RhH0ArhR4Ig2A9EoDaEAblAD6qL2kzhSwMQhPkvdjyWqxYOrIm38bc/P97MbeFBfrccRwtQS2mi51SGqBv1pbbc6sn0NS3kIPAYYowlTiAAyTd7drAVQ4AnXsAtIHVrRqOHRRTRE8lymsDt+X23LalctIWchDL8R3nKSRHqqnhQyA85eSLahYiOL79pfku4GiaaRBMNf8k4tHNNJRgbdZXUU47lLeSvcLh7vM7BitAYDFnB6r3WJoe6NgnGtfrOumQ0o6Haj9r7vne4bA+YaA6/OJOA8AKpMM1dgEoHcqkQ8o1LWWvcNRxfIbuuMpqKT5oTKa2NdaOrz8IHN+JXvMJJ7gzCSfhBASCqrScHuB8+/ZtePPmzd6Orn4YEtyA1VbltApuXcJJOAGBoCotJ+EEBIKqtJy1wWGXrd9R8TqG312Vdt7Eh/jiNlHEmk4w9tGq7iyHcAbxG2IzAOFQ3MYC4pwYDnWcK/4zJcQxSuVfhe7g0C8AeSH8aYNZhExtHn3/ptS3MTffJZzSIDwMrMa/WlY4tXT9krJVwCG+DAxNGU0p5TVwlfs3F6qfm3YLhymDsyVojsO1IATBD7b2mtjrTc13CwcYQMDh4ktw0gL018PxdxdAYy/+BO3op5WH450tPggYVryOrVty3u208oPxbzyxJBZ+Vo7+UY6PYdD6HRXfB2S17C0F/4Mf4hsa6HCNfaJZaEvPu7Mc/AVPKtY1OsiX/AiAsBb0SOWwl8Lw13UHx3fwkPmEE9BPOAknIBBUpeUknIBAUJWWk3ACAkFVt5ZDNJC/WKC/XlAbAwu/MZ3atWPl3cEBirYLhEZZ/bIt0F9A0YDQo4w69Ei5rqV0CcdvF7SP8t84ZW+leDPbC/JWZ1tQ3cGpDQgLYmcu8b+ZoJxNq/1ljXSXpquAg3UQ6JJVYCVMIx/PUbBrKQx/Xbdw5Gj5UjfWgOVoCgmC8hqUyj001c9Nu4UjR4yFYDX2d56CUBpsyaJKelPKuoVjO8/7KZwtjhoRnL/WciwczvE3vKZBgFKykBo039bU/Cosh8EAB+uR1J5WlLeS7uDgiH1IlDxO2T7K9djW1CLFsihvJd3BwUKYMsBgBaxVsH1aafBy2pGOdJek3cFhEFgK/oP3UKTekuxAsTQcNmlr6RJO60EubS/hBOQSTsIJCARVaTlrgfPjx4/h5uamyXF0v5oBzuPjY5Pj6OAEFn6QqvQ5AfaEk3ACAkFVWk7CCQgEVau2HHbrfCeQkAV/5kqxnWC8s6pWC4cQBcEtYjoEuEjJtwS0Wjilr9UCyEYLZ5lJQXm1cIgWEgyzQl5BeFu+9HyVcJhS0duHKHI4B9Qq4egVjB9oDZrXm5o/Kjg445JFTYXh9VYNxz+ZZFGtgu2rhMMdLlkIbyEobyXtWmrVo4nt8G0u/wKPxzjlrWS1cGQlfPuCp9Ne/0tRK/q7bId1De/GmUqkft2z7Wev1nK2HfiU6xNOQCnhJJyAQFCVlpNwAgJBVVpOwgkIBFVpOQknIBBUpeUknIBAUJWWk3ACAkHVP/iljLULIyeWAAAAAElFTkSuQmCC[/img][/td][/tr][/table][table][tr][td]A. [math]330=33(10)+0[/math][/td][td]B. [math]330=4(82)+2[/math][/td][td]C. [math]330=5(66)+0[/math][/td][/tr][/table]
Consider the polynomial function [math]f(x)=x^4-ux^3+24x^2-32x+16[/math][size=150] where [math]u[/math] is an unknown real number.[/size] [br]If [math]x-2[/math] is a factor, what is the value of[math]u[/math]? Explain how you know.
[size=150]Here are some diagrams that show the same third-degree polynomial, [math]P(x)=2x^3+5x^2+x+10[/math], divided by a linear factor and by a quadratic factor.[/size][size=150][br][table][tr][td][math]\frac{P(x)}{x+3}[/math][/td][td][img]data:image/png;base64,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[/img][/td][/tr][tr][td][math]\frac{P(x)}{x^2-x}[/math][/td][td][img]data:image/png;base64,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[/img][/td][/tr][/table][/size]What is the remainder of each of these divisions?
For each division, how does the degree of the remainder compare to the degree of the divisor?[br]
Could the remainder ever have the same degree as the divisor, or a higher degree? Give an example to show that this is possible, or explain why it is not possible.[br]
[size=150]Which of these polynomials could have [math](x-2)[/math] as a factor?[/size]
[size=150]Select one of the polynomials that you said doesn’t have [math](x-2)[/math] as a factor.[/size][br][br]Explain how you know [math](x-2)[/math] is not a factor.[br]
If you have not already done so, divide the polynomial by [math](x-2)[/math]. What is the remainder?[br]
List the remainders for each of the polynomials when divided by [math](x-2)[/math]. How do these values compare to the value of the functions at [math]x=2[/math]?[br]

IM Alg2.2.15 Practice: The Remainder Theorem

For the polynomial function [math]f(x)=x^3-2x^2-5x+6[/math] we have [math]f(0)=6,f(2)=\text{-}4,f(\text{-}2)=0,f(3)=0,f(\text{-}1)=8,f(1)=0[/math]. Rewrite [math]f(x)[/math] as a product of linear factors.
Select [b]all[/b] the polynomials that have [math](x-4)[/math] as a factor.
Write a polynomial function, [math]p(x)[/math], with degree 3 that has [math]p(7)=0[/math].
Long division was used here to divide the polynomial function [math]p(x)=x^3+7x^2-20x-110[/math] by [math](x-5)[/math] and to divide it by [math](x+5)[/math].[br][img]data:image/png;base64,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[/img][br]What is [math]p(\text{-}5)[/math]?
What is [math]p(5)[/math]?
Which polynomial function has zeros when [math]x=5,\frac{2}{3},\text{-}7[/math]?
The polynomial function [math]q(x)=3x^4+8x^3-13x^2-22x+24[/math] has known factors [math](x+3)[/math] and [math](x+2)[/math]. [br]Rewrite [math]q(x)[/math] as the product of linear factors. You can use the applet below to show your work.
We know these things about a polynomial function f(x): it has degree 3, the leading coefficient is negative, and it has zeros at x=-5,-1,3. Sketch a graph of f(x) given this information.

Information