Ugur's copy of Factorising Quadratic Equations with $x^2$ Coefficients of 1

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$x^2$ Coefficients of 1.

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

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Question statement

Factorise the following quadratic equations.

Give any introductory information the student needs.

			Name	Type	Generated Value

v1	integer	6
v2	integer	3
v3	integer	-2
v4	integer	9
v5	integer	2
v6	integer	-2

			Name	Type	Generated Value

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Value

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Generated value: `integer`

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Parts

Part a) Gap-fill
1. Gap Mathematical expression
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Part b) Gap-fill
1. Gap Mathematical expression
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Part c) Gap-fill
1. Gap Mathematical expression
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$\simplify{x^2+{v1+v2}x+{v1*v2}=0}$

Unnamed gap $=0$

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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Ugur's copy of Factorising Quadratic Equations with $x^2$ Coefficients of 1

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Ugur Efem 3 years, 4 months ago

Ugur Efem 3 years, 4 months ago

Ugur Efem 3 years, 4 months ago

Error in variable testing condition

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Generated value: `integer`

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b)

c)

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Ugur's copy of Factorising Quadratic Equations with x2x^2 Coefficients of 1

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Taxonomy: mathcentre

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Ugur Efem 3 years, 4 months ago

Ugur Efem 3 years, 4 months ago

Ugur Efem 3 years, 4 months ago

Error in variable testing condition

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Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

Ugur's copy of Factorising Quadratic Equations with $x^2$ Coefficients of 1

Generated value: `integer`