Polynomials: Expand and Simplify 1a

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Ben McGovern

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Name	Status	Author	Last Modified
Polynomials: Expand and Simplify 1a	Ready to use	Ben McGovern	14/08/2023 15:48
Polynomials: Expand and Simplify 1b	Ready to use	Ben McGovern	14/08/2023 15:52
Polynomials: Expand and Simplify 1c	Ready to use	Ben McGovern	14/08/2023 15:53
Polynomials: Expand and Simplify 1d	Ready to use	Ben McGovern	14/08/2023 16:15
Polynomials: Expand and Simplify 1e	Ready to use	Ben McGovern	14/08/2023 16:17
Polynomials: Expand and Simplify 2c	Ready to use	Ben McGovern	14/08/2023 16:21
Polynomials: Expand and Simplify 2b	Ready to use	Ben McGovern	14/08/2023 16:21
Polynomials: Expand and Simplify 2d	Ready to use	Ben McGovern	14/08/2023 16:21
Cubics: Finding a Quadratic Factor 1	Ready to use	Ben McGovern	14/09/2022 15:45
Cubics: Finding Linear Factors	Ready to use	Ben McGovern	14/08/2023 15:39
Polynomials: Expand and Simplify 2a	Ready to use	Ben McGovern	14/08/2023 16:19

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Question statement

Given two functions,

$f(x) = \simplify{{a1}x^2+{b1}x+{c1}}, \quad g(x)=\simplify{{a2}x^2+{b2}x+{c2}},$

calculate

$\simplify{{m}f(x)+{n}g(x)}.$

Give any introductory information the student needs.

			Name	Type	Generated Value

a1	integer	2
a2	integer	1
b1	integer	8
b2	integer	6
c1	integer	0
c2	integer	9
m	integer	3
n	integer	2

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Substituting the functions $f(x) = \simplify{{a1}x^2+{b1}x+{c1}}$ and $g(x)=\simplify{{a2}x^2+{b2}x+{c2}}$ into $\simplify{{m}f(x)+{n}g(x)}$ :

$\simplify{{m}f(x)+{n}g(x)} = \simplify{{m}({a1}x^2+{b1}x+{c1})+{n}({a2}x^2+{b2}x+{c2})}.$

Multiplying out the brackets and collecting similar terms:

$\begin{split}\simplify{{m}({a1}x^2+{b1}x+{c1})+{n}({a2}x^2+{b2}x+{c2})}&\,=\simplify[all, !cancelTerms,!collectNumbers]{{m*a1}x^2+{m*b1}x+{m*c1}+{n*a2}x^2+{n*b2}x+{n*c2}} \\ &\,=\simplify[all, !noLeadingminus]{{m*a1}x^2+{m*b1}x+{m*c1}+{n*a2}x^2+{n*b2}x+{n*c2}}\end{split}$

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Ben McGovern 2 years, 7 months ago

Ben McGovern 3 years, 9 months ago

Ben McGovern 4 years, 9 months ago

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Polynomials: Expand and Simplify 1a

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben McGovern 2 years, 7 months ago

Ben McGovern 3 years, 9 months ago

Ben McGovern 4 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `integer`