Factorising Quadratic Expressions

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Ed Southwood 6 years, 5 months ago

Created this as a copy of Factorising Quadratic Equations with

Name	Status	Author	Last Modified
Factorising Quadratic Equations with $x^2$ Coefficients of 1	Ready to use	Hannah Aldous	20/11/2019 14:39
Solving Quadratic Equations with $x^2$ Coefficients of 1 by Factorising	Should not be used	Hannah Aldous	20/11/2019 14:42
Katherine's copy of Factorising Quadratic Equations with $x^2$ Coefficients of 1	draft	Katherine Tomlinson	02/08/2017 12:44
Peter's copy of Factorising Quadratic Equations with $x^2$ Coefficients of 1	draft	Peter Knowles	12/09/2017 12:29
MATH6058 Factorising Quadratic Equations with $x^2$ Coefficients of 1	draft	Catherine Palmer	27/01/2020 17:30
Ida's copy of Factorising Quadratic Equations with $x^2$ Coefficients of 1	draft	Ida Landgärds	13/04/2018 09:15
Ida's copy of Solving Quadratic Equations with $x^2$ Coefficients of 1 by Factorising	Doesn't work	Ida Landgärds	19/04/2018 12:00
løs og faktorisere andregradslikninga	draft	Ida Landgärds	02/12/2020 15:42
spørsmål 6	draft	Ida Landgärds	02/12/2020 15:42
Quadratic Formula	draft	Blathnaid Sheridan	19/09/2024 11:51
Blathnaid's copy of spørsmål 6	draft	Blathnaid Sheridan	02/12/2020 15:42
Blathnaid's copy of spørsmål 6	draft	Blathnaid Sheridan	02/12/2020 15:42
Ed's copy of Factorising Quadratic Equations with $x^2$ Coefficients of 1	draft	Ed Southwood	08/08/2022 10:18
Factorising Quadratic Expressions	draft	Ed Southwood	08/08/2022 10:18
Simon's copy of Factorising Quadratic Equations with $x^2$ Coefficients of 1	draft	Simon Thomas	07/03/2019 09:52
what the heck?	draft	John Wick	30/05/2019 11:33
Factorizing Quadratic Equations with $x^2$ Coefficients of 1	draft	Xiaodan Leng	10/07/2019 21:45
Factorizing Quadratic Equations with $x^2$ Coefficients of 1	draft	Xiaodan Leng	10/07/2019 21:45
Musa's copy of 3 Factorising Quadratic Equations with $x^2$ Coefficients of 1	draft	Musa Mammadov	27/06/2023 01:26
Ugur's copy of Factorising Quadratic Equations with $x^2$ Coefficients of 1	Ready to use	Ugur Efem	08/11/2021 16:44
Factorising quadratics EXAM	Ready to use	Yvonne Wancke	17/04/2023 11:42
Factorising quadratics S1MT2	Ready to use	Yvonne Wancke	22/03/2023 11:35
AD1 Factorising a Quadratic (a=1)	Ready to use	Andrew Neate	09/04/2024 15:13

There are 65 other versions that do you not have access to.

Question statement

Factorise the following quadratic expressions.

Give any introductory information the student needs.

			Name	Type	Generated Value

v1	integer	8
v2	integer	3
v3	integer	-8
v4	integer	3
v5	integer	2
v6	integer	-2

			Name	Type	Generated Value

Automatically regenerate variables?

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Data type

Value

xxxxxxxxxx
 
random(1..10)

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Description

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

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Generated value: `integer`

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Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) 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.

$\simplify{x^2+{v1+v2}x+{v1*v2}}$

Unnamed gap

Advice

Quadratic equations of the form

$x^2+bx+c=0$

can be factorised to create an equation of the form

$(x+m)(x+n)=0\text{.}$

When we expand a factorised quadratic expression we obtain

$(x+m)(x+n)=x^2+(m+n)x+(m \times n)\text{.}$

To factorise an equation of the form $x^2+bx+c$ , we need to find two numbers which add together to make $b$ , and multiply together to make $c$ .

a)

$\simplify{x^2+{v1+v2}x+{v1*v2}=0}$

We need to find two values that add together to make $\var{v1+v2}$ and multiply together to make $\var{v1*v2}$ .

$\begin{align} \var{v1} \times \var{v2}&=\var{v1*v2}\\ \var{v1}+\var{v2}&=\var{v1+v2}\\ \end{align}$

So the factorised form of the equation is

$\simplify{(x+{v1})(x+{v2})}=0\text{.}$

b)

We can begin factorising by finding factors of $\var{v3*v4}$ that add together to give $\var{v3+v4}$ .

$\begin{align} \var{v3} \times \var{v4}&=\var{v3*v4}\\ \var{v3}+\var{v4}&=\var{v3+v4}\\ \end{align}$

So the factorised form of the equation is

$\simplify{(x+{v3})(x+{v4})}=0\text{.}$

c)

When factorising the quadratic expression

$\simplify{x^2+{v5*v6}=0}$

we need to find two values that add together to make $0$ and multiply together to make $\var{v5*v6}$ .

$\begin{align} \var{v5} \times \var{v6}& = \var{v5*v6}\\ \simplify[]{ {v5} + {v6}} &= 0 \\ \end{align}$

So the factorised form of the equation is

$\simplify{(x+{v5})(x+{v6})}=0\text{.}$

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This question is used in the following exam:

MA10103 Test 1 by Ed Southwood in Ed's workspace.

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Ed Southwood 6 years, 5 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

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Factorising Quadratic Expressions

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Ed Southwood 6 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

Generated value: `integer`