J. Richard's copy of Extract common factors of polynomials

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J. Richard Snape 6 years, 6 months ago

Created this as a copy of Extract common factors of polynomials.

Name	Status	Author	Last Modified
Extract common factors of polynomials	Has some problems	Bradley Bush	20/11/2019 14:38
Marlon's copy of Extract common factors of polynomials	draft	Marlon Arcila	03/02/2018 16:28
Joël's copy of Extract common factors of polynomials	draft	Jo Cohen	02/12/2020 15:42
J. Richard's copy of Extract common factors of polynomials	draft	J. Richard Snape	26/09/2018 13:55
J. Richard's copy of Extract common factors of polynomials	draft	J. Richard Snape	03/10/2019 10:26

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Question statement

An expression can be factorised by finding common factors of each term in the expression.

Completely factorise the following expressions by finding their common factors.

Make sure that you include a multiplication symbol * between each algebraic variable, and before brackets, e.g. a*b*(x+1) instead of ab(x+1). Otherwise, the system might not accept your answer.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	list	List of 50 items
b	list	List of 50 items
c	list	List of 50 items
x1	integer	5
x2	integer	5
x3	integer	4
x4	integer	-5
x5	integer	1
x6	integer	4
x7	integer	3

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random([3, 11, 17, 29, 37, 43] except b),50)

JME function reference

Description

Vector of every other random prime number

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

Can an exam override the value of this variable?

Generated value: `list`

[ 3, 11, 11, 29, 37, 37, 3, 17, 3, 11, 43, 37, 43, 29, 3, 43, 29, 17, 29, 29, 29, 29, 3, 3, 37, 43, 43, 3, 3, 43, 17, 11, 43, 29, 11, 11, 3, 11, 37, 29, 29, 3, 3, 37, 43, 11, 17, 37, 11, 3 ]

← Depends on:

→ Used by:

Advice
"Part a)" - prompt
"Part a)" → "Unnamed gap" - Correct answer
"Part b)" - prompt
"Part b)" → "Unnamed gap" - Correct answer
"Part c)" - prompt
"Part c)" → "Unnamed gap" - Correct answer
"Part d)" - prompt
"Part d)" → "Unnamed gap" - Correct answer
"Part e)" - prompt
"Part e)" → "Unnamed gap" - Correct answer

Parts

Part a) Gap-fill
1. Gap Mathematical expression
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Part b) Gap-fill
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Part c) Gap-fill
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Part d) Gap-fill
1. Gap Mathematical expression
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Part e) Gap-fill
1. Gap Mathematical expression
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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

$\simplify{{2*a[0]}x+{2*b[0]}}=$ Unnamed gap

Advice

In order to factorise the expressions, the factors that make up each term in the expression need to be identified and, where these factors are the same for all terms in the expression, those factors can be taken outside the brackets. Stop when the remaining terms have no more common factors.

a)

Both terms have a common factor of $2$ .

$\begin{align} \simplify{2{a[0]}x+2{b[0]}}&= (\simplify[]{2{a[0]}})x+2\times\var{b[0]}\\ &=\simplify[]{2({a[0]}x+{b[0]})} \end{align}$

b)

Both terms have common factors of $6$ and $y$ .

$\begin{align} \simplify{6{a[1]}y+6{b[1]}y^2}&= 6 \times \var{a[1]} y + 6 \times \var{b[1]} y^2 \\ &= 6 \times (\simplify{{a[1]}y + {b[1]}y^2}) \\ &=6y(\simplify[]{{a[1]}+{b[1]}y}) \end{align}$

c)

Both terms have common factors of $x$ , $y$ and $z$ .

$\begin{align} \simplify{{a[2]}x*y*z+{b[2]}x^2y^2z^2}&=\var{a[2]} \times xyz + \var{b[2]} \times xyz \times xyz\\ &=xyz(\var{a[2]} + \var{b[2]} xyz) \end{align}$

d)

All three terms have a common factor of $5$ .

$\begin{align} \simplify{5{a[3]}d+5{b[3]}r+5m}&= 5 \times \var{a[3]} d+5 \times \var{b[3]} r + 5 m \\ &=\simplify[]{5({a[3]}d+{b[3]}r+m)} \end{align}$

e)

All the terms have common factors of $6$ , $c$ and $d$ .

$\begin{align} \simplify{6{a[4]}cd^2+6{b[4]}c^2d+6{c[1]}c^2d^2} &= 6 \times \var{a[4]} c d^2 \;+\; 6 \times \var{b[4]} c^2 d \;+\; 6 \times \var{c[1]} c^2 d^2 \\ &= 6(\var{a[4]} c d^2 + \var{b[4]} c^2 d + \var{c[1]} c^2 d^2) \\ &=6cd(\var{a[4]}d+\var{b[4]}c+\var{c[1]}cd) \end{align}$

Give a worked solution to the whole question.

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J. Richard's copy of Extract common factors of polynomials

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Taxonomy: mathcentre

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Checkpoint description

J. Richard Snape 6 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

a)

b)

c)

d)

e)

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Error

J. Richard's copy of Extract common factors of polynomials

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

J. Richard Snape 6 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

a)

b)

c)

d)

e)

Generated value: `list`