Algebra III: factorisation (HCF of polynomials)

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8 years, 7 months ago

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Nasir Firoz Khan 8 years, 7 months ago

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Nasir Firoz Khan 8 years, 7 months ago

Created this as a copy of Algebra III: factorisation.

Name	Status	Author	Last Modified
Factorisation	Ready to use	Katie Lester	01/06/2016 09:47
Linear factorisation - Summative test	Ready to use	Jinhua Mathias	28/08/2024 12:15
Linea factorisation - Summative test	draft	steve kilgallon	10/11/2020 09:18
Factorisation	draft	steve kilgallon	23/08/2017 16:29
Algebra III: factorisation	Ready to use	Luke Park	14/09/2017 15:37
Algebra III: factorisation (HCF of polynomials)	Ready to use	Nasir Firoz Khan	12/08/2016 16:13
EXAM 1 Linea factorisation	draft	steve kilgallon	30/08/2016 12:31
Algebra III: factorisation	draft	Nasir Firoz Khan	31/08/2016 14:00
Torris's copy of Algebra III: factorisation	Ready to use	Torris Bakke	16/06/2022 14:46
Richard's copy of Algebra III: factorisation	draft	Richard Miles	14/09/2016 10:29
Mock exam Linea factorisation - Summative test	draft	steve kilgallon	04/11/2017 14:21
Factorisation	draft	Rachel Staddon	20/04/2017 15:33
Marlon's copy of Mock exam Linea factorisation - Summative test	draft	Marlon Arcila	03/02/2018 16:10
Marlon's copy of Algebra III: factorisation	draft	Marlon Arcila	03/02/2018 16:16
Marlon's copy of Factorisation	draft	Marlon Arcila	03/02/2018 16:17
Marlon's copy of Factorisation	draft	Marlon Arcila	03/02/2018 16:30
Algebra III: factorisation	Ready to use	heike hoffmann	14/11/2018 20:53
Shivram's copy of Algebra III: factorisation	draft	Shivram Venkat	09/06/2019 23:04
Tom's copy of Algebra III: factorisation	draft	Tom Bold	18/06/2019 12:42

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Question statement

Factorise the following expressions by taking out the highest common factor.

Make sure you input an asterisk (*) for multiplication wherever necessary.

For example, $xy$ should be written as $x$ * $y$ , and $a(b+c)$ should be written as $a$ * $(b+c)$ .

write $x^2$ as $x$ ^2

Give any introductory information the student needs.

			Name	Type	Generated Value

c	list	[ 14, 6, 10, 8, 2, 2 ]
c2	list	[ 9, 3, 6, 15, 3 ]
c3	list	[ 2, 4, 10 ]
squares	list	[ 2, 6 ]
firstsquare	number	4
secondsquare	number	36

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
shuffle([2,2,6,8,10,14])

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Description

Coefficients in a,b,c (HCF: 2)

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `list`

[ 14, 6, 10, 8, 2, 2 ]

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Advice

An expression like the one seen in part h) is known as the difference of two squares, i.e. it is of the form $a^2 - b^2$ . A very useful result to know is the factorisation of the difference of two squares:

$a^2 - b^2 = (a+b)(a-b)$

We can check that this is correct:

$(a+b)(a-b) = a^2 + ba -ab -b^2$

Since multiplication is a commutative operation, i.e. the order is not important, we have that $ba = ab$ , so the middle terms cancel each other out. Therefore:

$a^2 + ba -ab -b^2 = a^2 - b^2$

It can be easy to forget about this handy result. A clue is the use of a square number you are expected to know, such as 36, 64, 81 etc. It is not always as obvious if more algebra is involved, e.g. $f^2 - g^6h^4 = (f + g^3h^2)(f-g^3h^2)$ .

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Algebra III: factorisation (HCF of polynomials)

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Nasir Firoz Khan 8 years, 7 months ago

Nasir Firoz Khan 8 years, 7 months ago

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Algebra III: factorisation (HCF of polynomials)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Nasir Firoz Khan 8 years, 7 months ago

Nasir Firoz Khan 8 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `list`