Polynomials: equating coefficients 1

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Ben Brawn

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7 years, 6 months ago

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Name	Status	Author	Last Modified
Polynomials: equating coefficients 1	Ready to use	Ben Brawn	14/09/2017 07:39
Polynomials: equating coefficients 1	draft	Paul Hancock	24/07/2018 02:36
Polynomials: equating coefficients 1 [L4 Randomised]	Needs to be tested	Matthew James Sykes	25/07/2018 11:02

There is one other version that you do not have access to.

Question statement

Suppose that during some working, you find that

{poly} $=$ {otherpoly}

for all $x$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

k	list	[ -1, 0, 0, -2, 0, 0, 0, 0 ]
n	integer	3
poly	string	$\simplify{{k[0]}+{k[1]}x+{k[2
otherpoly	string	$\simplify{C_0+{j[0]}+({j[1]}C
j	list	[ -4, 1, -5, -11, -3, -2, 3 ]

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random(0,random(-12..12 except 0)),n)+[random(-12..12 except 0)]+[0,0,0,0]

JME function reference

Description

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`

[ -1, 0, 0, -2, 0, 0, 0, 0 ]

← Depends on:

→ Used by:

poly

Advice
"Unnamed part" → "Gap 0." - Minimum accepted value
"Unnamed part" → "Gap 0." - Maximum accepted value
"Unnamed part" → "Gap 1." - Minimum accepted value
"Unnamed part" → "Gap 1." - Maximum accepted value
"Unnamed part" → "Gap 2." - Minimum accepted value
"Unnamed part" → "Gap 2." - Maximum accepted value
"Unnamed part" → "Gap 3." - Minimum accepted value
"Unnamed part" → "Gap 3." - Maximum accepted value
"Unnamed part" → "Gap 4." - Minimum accepted value
"Unnamed part" → "Gap 4." - Maximum accepted value
"Unnamed part" → "Gap 5." - Minimum accepted value
"Unnamed part" → "Gap 5." - Maximum accepted value

Parts

Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
5. Gap Gap 4. Number entry
  Add
6. Gap Gap 5. Number entry
  Add

Gap-fill

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

What can be said about the value of $C_i$ ?

$C_0=$ Gap 0., $C_1=$ Gap 1., $C_2=$ Gap 2., $C_3=$ Gap 3., $C_4=$ Gap 4., $C_5=$ Gap 5.

Advice

Two polynomials are equal if and only if their corresponding coefficients are also equal.

So we 'equate the coefficients' of the polynomials given in this question, this means that the constant terms must be equal, ie

$\simplify{{k[0]}=C_0+{j[0]}}$

the coefficients of the $x$ terms must be equal, ie

$\simplify{{k[1]}={j[1]}C_1+{j[2]}}$

the coefficients of the $x^2$ terms must be equal, ie

$\simplify{{k[2]}=C_2}$

the coefficients of the $x^3$ terms must be equal, ie

$\simplify{{k[3]}={j[3]}C_3}$

the coefficients of the $x^4$ terms must be equal, ie

$\simplify{{k[4]}=C_4/{j[4]}}$

and the coefficients of the $x^5$ terms must be equal, ie

$\simplify{{k[5]}=C_5/{j[5]}+{j[6]}}.$

Solving equal of these equations for $C_i$ gives our required values.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
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This question is used in the following exams:

Equating coefficients by Ben Brawn in Algebra.
4 Equating coefficients by Ben Brawn in numbas talk 2022.
Graphing and Polynomials by Chris Templet in Chris's workspace.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Ben Brawn 7 years, 6 months ago

Ben Brawn 7 years, 6 months ago

Ben Brawn 7 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

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Polynomials: equating coefficients 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben Brawn 7 years, 6 months ago

Ben Brawn 7 years, 6 months ago

Ben Brawn 7 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`