Polynomial Division (Part 1): IM Alg2.2.12
[url=https://im.kendallhunt.com/HS/teachers/3/2/12/preparation.html]“Polynomial Division (Part 1)”[/url] from IM Algebra II © 2019 [url=https://www.illustrativemathematics.org/]Illustrative Mathematics[/url]. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0[/url] license.
Table of Contents
- Alg2.2.12 Lesson
- IM Alg2.2.12 Lesson: Polynomial Division (Part 1)
- Alg2.2.12 Practice
- IM Alg2.2.12 Practice: Polynomial Division (Part 1)
IM Alg2.2.12 Lesson: Polynomial Division (Part 1)
What do you notice? What do you wonder?
[table][tr][td]A. [math](x-3)(x+5)=x^2+2x-15[/math][/td][td][img]data:image/png;base64,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[/img][/td][/tr][tr][td]B. [math](x-1)(x^2+3x-4)=x^3+2x^2-7x+4[/math][/td][td][img]data:image/png;base64,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[/img][/td][/tr][tr][td]C. [math](x-2)(?)=(x^3-x^2-4x+4)[/math][/td][td][img]data:image/png;base64,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[/img][/td][/tr][/table]
[size=150]Priya wants to sketch a graph of the polynomial [math]f[/math] defined by [math]f(x)=x^3+5x^2+2x-8[/math]. [br]She knows [math]f(1)=0[/math], so she suspects that [math](x-1)[/math] could be a factor of [math]x^3+5x^2+2x-8[/math] and writes [math](x^3+5x^2+2x-8)=(x-1)(?x^2+?x+?)[/math][math](x^3+5x^2+2x-8)=(x-1)(?x^2+?x+?)[/math] and draws a diagram.[/size]
Finish Priya’s diagram.
Write [math]f(x)[/math] as the product of [math](x-1)[/math] and another factor.[br]
Write [math]f(x[/math]) as the product of three linear factors.[br]
Make a sketch of y=f(x).
Here are some polynomial functions with known factors. Rewrite each polynomial as a product of linear factors. Note: you may not need to use all the columns in each diagram. For some problems, you may need to make another diagram.
[math]A(x)=x^3-7x^2-16x+112,(x-7)[/math]
[math]B(x)=2x^3-x^2-27x+36,(x-\frac{3}{2})[/math]
[math]C(x)=x^3-3x^2-13x+15,(x+3)[/math][br]
[math]D(x)=x^4-13x^2+36,(x-2),(x+2)[/math][br](Hint: [math]x^4-13x^2+36=x^4+0x^3-13x^2+0x+36[/math])
[math]F(x)=4x^4-15x^3-48x^2+109x+30,(x-5),(x-2),(x+3)[/math]
A diagram can also be used to divide polynomials even when a factor is not linear.
Suppose we know [math](x^2-2x+5)[/math] is a factor of [math]x^4+x^3-5x^2+23x-20[/math]. [br]We could write [math](x^4+x^3-5x^2+23x-20)=(x^2-2x+5)(?x^2+?x+?)[/math].
Make a diagram and find the missing factor.
IM Alg2.2.12 Practice: Polynomial Division (Part 1)
[size=150]The polynomial function [math]p(x)=x^3-3x^2-10x+24[/math] has a known factor of [math](x-4)[/math].[/size][br][br]Rewrite [math]p(x)[/math] as the product of linear factors.
Draw a rough sketch of the graph of the function.
[size=150]Tyler thinks he knows one of the linear factors of [math]P(x)=x^3-9x^2+23x-15[/math]. After finding that [math]P(1)=0[/math], he suspects that[math]x-1[/math] is a factor of [math]P(x)[/math]. [/size][br][img]data:image/png;base64,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[/img][br]Here is the diagram he made to check if he’s right, but he set it up incorrectly. What went wrong?
The polynomial function [math]q(x)=2x^4-9x^3-12x^2+29x+30[/math] has known factors [math](x-2)[/math] and [math](x+1)[/math]. Which expression represents [math]q(x)[/math] as the product of linear factors?
[size=150]Each year a certain amount of money is deposited in an account which pays an annual interest rate of [math]r[/math] so that at the end of each year the balance in the account is multiplied by a growth factor of [math]x=1+r[/math]. $1,000 is deposited at the start of the first year, an additional $300 is deposited at the start of the next year, and $500 at the start of the following year.[/size][br][br]Write an expression for the value of the account at the end of three years in terms of the growth factor [math]x[/math].[br]
Determine (to the nearest cent) the amount in the account at the end of three years if the interest rate is 4%.[br]
[size=150]State the degree and end behavior of [math]f(x)=5+7x-9x^2+4x^3[/math].[/size]
Explain or show your reasoning.
[size=150]Describe the end behavior of [math]f(x)=1+7x+9x^3+6x^4-2x^5[/math].[/size][br]
[size=150]What are the points of intersection between the graphs of the functions [math]f(x)=(x+3)(x-1)[/math] and [math]g(x)=(x+1)(x-3)[/math]?[/size]