smc-4357-50-Factorise

Algebraic Techniques, SMB-066

Factorise the expression `-12y^2+18y-6` (2 marks)

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`6(2y-1)(1-y)\ \ text(or)\ \ 6(1-2y)(y-1)`

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`-12y^2+18y-6=-6(2y^2-3y+1)`

`-6(2y^2-3y+1)=>\ \ `	`text{P}`	`=2xx1=2`
	`text{S}`	`=-3`
	`text{F}`	`=-2,-1`

`-6(2y^2-3y+1)`	`=(-6(2y-1)(2y-2))/2`
	`=-6(2y-1)(y-1)`
	`=6(2y-1)(1-y)\ \ text(or)\ \ 6(1-2y)(y-1)`

Algebraic Techniques, SMB-065

Fully factorise the expression `6y^2+10y-4` (2 marks)

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`2(3y-1)(y+2)`

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`6y^2+10y-4=2(3y^2+5y-2)`

`2(3y^2+5y-2)=>\ \ `	`text{P}`	`=3xx-2=-6`
	`text{S}`	`=5`
	`text{F}`	`=-1,6`

`2(3y^2+5y-2)`	`=(2(3y-1)(3y+6))/3`
	`=2(3y-1)(y+2)`

Algebraic Techniques, SMB-064

Factorise the expression `2x^2+x-6` (2 marks)

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`(2x-3)(x+2)`

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`2x^2+x-6=>\ \ `	`text{P}`	`=2xx-6=-12`
	`text{S}`	`=1`
	`text{F}`	`=-3,4`

`2x^2+x-6`	`=((2x-3)(2x+4))/2`
	`=(2x-3)(x+2)`

Algebraic Techniques, SMB-063

Fully factorise the expression `3a^2+12ab-2a-8b` (2 marks)

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`(3a-2)(a+4b)`

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`3a^2+12ab-2a-8b`	`=3a(a+4b)-2(a+4b)`
	`=(3a-2)(a+4b)`

Algebraic Techniques, SMB-062

Fully factorise the expression `2x^2-6xy-3x+9y` (2 marks)

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`(2x-3)(x-3y)`

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`2x^2-6xy-3x+9y`	`=2x(x-3y)-3(x-3y)`
	`=(2x-3)(x-3y)`

Algebraic Techniques, SMB-061

Factorise the expression `5b^3-5b` (2 marks)

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`5b(b+1)(b-1)`

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`5b^3-5b`	`=5b(b^2-1)`
	`=5b(b+1)(b-1)`

Algebraic Techniques, SMB-048

Factorise the expression `b^2+4b-12` (2 marks)

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`(b+6)(b-2)`

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`b^2+4b-12=(b+6)(b-2)`

Algebraic Techniques, SMB-047

Factorise the expression `-a^2+3a+10` (2 marks)

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`-(a+2)(a-5)\ \ text(or)\ \ (5-a)(a+2)`

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`-a^2+3a+10`	`=-(a^2-3a-10)`
	`=-(a-5)(a+2)`
	`=(5-a)(a+2)`

Algebraic Techniques, SMB-046

Factorise the expression `n^2+5n-24` (2 marks)

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`(n+8)(n-3)`

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`n^2+5n-24=(n+8)(n-3)`

Algebraic Techniques, SMB-045

Fully factorise the expression `6x^2-8x-8` (2 marks)

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`2(3x+2)(x-2)`

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`6x^2-8x-8=2(3x+2)(x-2)`

Algebraic Techniques, SMB-044

Factorise the expression `2p^2-5p-12` (2 marks)

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`(2p+3)(p-4)`

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`2p^2-5p-12=(2p+3)(p-4)`

Algebraic Techniques, SMB-043

Factorise the expression `y^2-2y-15` (2 marks)

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`(y+3)(y-5)`

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`y^2-2y-15=(y+3)(y-5)`

Algebraic Techniques, SMB-042

Factorise the expression `x^2+6x+8` (2 marks)

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`(x+2)(x+4)`

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`x^2+6x+8=(x+2)(x+4)`

Functions, 2ADV F1 2006 HSC 1b

Factorise `2x^2 + 5x-3`. (2 marks)

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`(2x-1) (x + 3)`

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`2x^2 + 5x-3= (2x-1) (x + 3)`