All Factoring Methods - Revision history

Iwiseman: Iwiseman moved page Factoring to All Factoring Methods

2026-04-23T02:27:36Z

← Older revision	Revision as of 02:27, 23 April 2026
(No difference)

2026-04-23T02:25:53Z

Synthetic Division

← Older revision		Revision as of 02:25, 23 April 2026
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	x³ + 3x² - 6x -8		x³ + 3x² - 6x -8
	This approach can only be used when dividing a polynomial by a binomial of the form x-b and linear divisor with leading coefficient of 1. So this means you cannot have 2x-b or 4x-b '''it must be x-b'''.		This approach can only be used when dividing a polynomial by a binomial of the form x-b and linear divisor with leading coefficient of 1. So this means you cannot have 2x-b or 4x-b '''it must be x-b'''.
			So next, we write down the possible factors of the constant (-8) and they are
			+/- 1,2,4,8
			Putting in -1 gives us zero (-1)³ + 3(-1)² - 6(-1) -8 so x+1 is a factor

			-1 \| 1 + 3 - 6 -8
			\| ↓ - 1 - 2 8
			---------------
			1 + 2 -8 = 0
			1x²+ 2x -8 = 0

2026-04-23T02:17:25Z

Synthetic Division

← Older revision		Revision as of 02:17, 23 April 2026
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	=Synthetic Division=		=Synthetic Division=
			This is very easy and a nice short cut. So we have
			x³ + 3x² - 6x -8
			This approach can only be used when dividing a polynomial by a binomial of the form x-b and linear divisor with leading coefficient of 1. So this means you cannot have 2x-b or 4x-b '''it must be x-b'''.

2026-04-23T02:08:12Z

Long Division

2026-04-23T02:07:58Z

Long Division

2026-04-23T02:07:12Z

Long Division

@@ Line 102: / Line 102: @@
   = (2x² - 1)(x² - 3)
 =Long Division=
 =Synthetic Division=

2026-04-20T07:30:12Z

2026-04-20T07:29:29Z

Factoring by Grouping

← Older revision		Revision as of 07:29, 20 April 2026
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	= (x + 3) (2x + 3)		= (x + 3) (2x + 3)
	Factoring a Quadratic Trinomial=		Factoring a Quadratic Trinomial=
	==Factoring a Quadratic Trinomial where (a = 1)==		=Factoring a Quadratic Trinomial where (a = 1)=
	Quadratics take the form		Quadratics take the form
	ax² + bx + c		ax² + bx + c
Line 32:		Line 32:
	Factors of -21 are -1,21, -3,7 - so 7-3 = 4		Factors of -21 are -1,21, -3,7 - so 7-3 = 4
	(x-7y)(x-3y)		(x-7y)(x-3y)
	==Factoring a Quadratic Trinomial (a <> 1)==		=Factoring a Quadratic Trinomial (a <> 1)=
	Quadratics take the form		Quadratics take the form
	ax² + bx + c		ax² + bx + c
Line 63:		Line 63:
	2[2x(x+4) - 5(x+4)]		2[2x(x+4) - 5(x+4)]
	2(x+4)(2 x+5)		2(x+4)(2 x+5)

	=Difference of Squares=		=Difference of Squares=
	The rule is:		The rule is:

2026-04-20T07:26:24Z

← Older revision		Revision as of 07:26, 20 April 2026
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	= 2x(x + 3) + 3(x + 3) Note (x+3) is common and is the GCF		= 2x(x + 3) + 3(x + 3) Note (x+3) is common and is the GCF
	= (x + 3) (2x + 3)		= (x + 3) (2x + 3)
	=Factoring a Quadratic Trinomial where (a = 1)=		Factoring a Quadratic Trinomial=
			==Factoring a Quadratic Trinomial where (a = 1)==
	Quadratics take the form		Quadratics take the form
	ax² + bx + c		ax² + bx + c
Line 31:		Line 32:
	Factors of -21 are -1,21, -3,7 - so 7-3 = 4		Factors of -21 are -1,21, -3,7 - so 7-3 = 4
	(x-7y)(x-3y)		(x-7y)(x-3y)
	=Factoring a Quadratic Trinomial (a <> 1)=		==Factoring a Quadratic Trinomial (a <> 1)==
	Quadratics take the form		Quadratics take the form
	ax² + bx + c		ax² + bx + c

2026-04-20T05:02:39Z

Factoring by Substitution