Synthetic Division of Polynomials - Revision history

Iwiseman at 01:47, 21 April 2026

2026-04-21T01:47:13Z

@@ Line 1: / Line 1: @@
 =Introduction=
 Needed to know this for [[Rational Zero Theorem]] so here goes
 =Example=
 So we start with

Iwiseman: Iwiseman moved page Synthetic Division to Synthetic Division of Polynomials

2026-04-21T01:05:55Z

Iwiseman moved page Synthetic Division to Synthetic Division of Polynomials

← Older revision	Revision as of 01:05, 21 April 2026
(No difference)

Iwiseman: /* Example */

2026-04-20T23:43:53Z

Example

← Older revision		Revision as of 23:43, 20 April 2026
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	(x³ -2x² -5x + 6) / (x-3)		(x³ -2x² -5x + 6) / (x-3)
	So to begin we list the coefficients of the functions in a row		So to begin we list the coefficients of the functions in a row
	\| 1 - 2 - 5 + 6		\| 1 - 2 - 5 + 6
	\|		\|
	-----------------		-----------------
	Next we solve the x-3, i.e x -3 = 0, therefore		Next we solve the x-3, i.e x -3 = 0, therefore
	x = 3		x = 3
	So first we bring down the 1		So first we bring down the 1
	3 \| 1 - 2 - 5 + 6		3 \| 1 - 2 - 5 + 6
	\| ↓		\| ↓
	-----------------		-----------------
	1		1
	Then we multiply the 3 by the number brought down (1) and place it under the next to the next coefficient		Then we multiply the 3 by the number brought down (1) and place it under the next to the next coefficient
	3 \| 1 - 2 - 5 + 6		3 \| 1 - 2 - 5 + 6
	\| ↓ 3		\| ↓ 3
	-----------------		-----------------
	1		1
	Add the coefficient to the result 3, i.e. -2 + 3 = 1		Add the coefficient to the result 3, i.e. -2 + 3 = 1
	3 \| 1 - 2 - 5 + 6		3 \| 1 - 2 - 5 + 6
	\| ↓ 3		\| ↓ 3
	-----------------		-----------------
	1 1		1 1
	Then we multiply the 3 by the number brought down (1)		Then we multiply the 3 by the number brought down (1)
	3 \| 1 - 2 - 5 + 6		3 \| 1 - 2 - 5 + 6
	\| ↓ 3 3		\| ↓ 3 3
	-----------------		-----------------
	1 1		1 1
	Add the coefficient to the result 3, i.e. -5 + 3 = -2		Add the coefficient to the result 3, i.e. -5 + 3 = -2
	3 \| 1 - 2 - 5 + 6		3 \| 1 - 2 - 5 + 6
	\| ↓ 3 3		\| ↓ 3 3
	-----------------		-----------------
	1 1 -2		1 1 -2
	Then we multiply the 3 by the number brought down (-2)		Then we multiply the 3 by the number brought down (-2)
	3 \| 1 - 2 - 5 + 6		3 \| 1 - 2 - 5 + 6
	\| ↓ 3 3 - 6		\| ↓ 3 3 - 6
	-----------------		-----------------
	1 1 -2		1 1 -2
	Add the coefficient to the result 3, i.e. 6 - 6 = 0		Add the coefficient to the result 3, i.e. 6 - 6 = 0
	3 \| 1 - 2 - 5 + 6		3 \| 1 - 2 - 5 + 6
	\| ↓ 3 3 - 6		\| ↓ 3 3 - 6
	-----------------		-----------------
	1 1 -2 0		1 1 -2 0
	If the you get a zero then		If the you get a zero then
	x - 3 is a factor and x =3		x - 3 is a factor and x =3
	So taking the last line and adding the power of x in line with the question we see		So taking the last line and adding the power of x in line with the question we see
	-----------------		-----------------
	1 1 -2 0		1 1 -2 0
	1x³+1x -2 <= This is the answer		1x³+1x -2 <= This is the answer

Iwiseman: /* Example */

2026-04-20T07:07:22Z

Example

← Older revision		Revision as of 07:07, 20 April 2026
Line 47:		Line 47:
	If the you get a zero then		If the you get a zero then
	x - 3 is a factor and x =3		x - 3 is a factor and x =3
			So taking the last line and adding the power of x in line with the question we see
			-----------------
			1 1 -2 0
			1x³+1x -2 <= This is the answer

Iwiseman: /* Introduction */

2026-04-20T07:04:03Z

Introduction

← Older revision		Revision as of 07:04, 20 April 2026
Line 1:		Line 1:
	=Introduction=		=Introduction=
	Needed to know this for [[Rational Zero Theorem]] so here goes		Needed to know this for [[Rational Zero Theorem]] so here goes
			=Example=
			So we start with
			(x³ -2x² -5x + 6) / (x-3)
			So to begin we list the coefficients of the functions in a row
			\| 1 - 2 - 5 + 6
			\|
			-----------------
			Next we solve the x-3, i.e x -3 = 0, therefore
			x = 3
			So first we bring down the 1
			3 \| 1 - 2 - 5 + 6
			\| ↓
			-----------------
			1
			Then we multiply the 3 by the number brought down (1) and place it under the next to the next coefficient
			3 \| 1 - 2 - 5 + 6
			\| ↓ 3
			-----------------
			1
			Add the coefficient to the result 3, i.e. -2 + 3 = 1
			3 \| 1 - 2 - 5 + 6
			\| ↓ 3
			-----------------
			1 1
			Then we multiply the 3 by the number brought down (1)
			3 \| 1 - 2 - 5 + 6
			\| ↓ 3 3
			-----------------
			1 1
			Add the coefficient to the result 3, i.e. -5 + 3 = -2
			3 \| 1 - 2 - 5 + 6
			\| ↓ 3 3
			-----------------
			1 1 -2
			Then we multiply the 3 by the number brought down (-2)
			3 \| 1 - 2 - 5 + 6
			\| ↓ 3 3 - 6
			-----------------
			1 1 -2
			Add the coefficient to the result 3, i.e. 6 - 6 = 0
			3 \| 1 - 2 - 5 + 6
			\| ↓ 3 3 - 6
			-----------------
			1 1 -2 0
			If the you get a zero then
			x - 3 is a factor and x =3

Iwiseman: /* Introduction */

2026-04-20T06:42:51Z

Introduction

← Older revision		Revision as of 06:42, 20 April 2026
Line 1:		Line 1:
	=Introduction=		=Introduction=
	Needed to know this for [Rational Zero Theorem] so here goes		Needed to know this for [[Rational Zero Theorem]] so here goes

Iwiseman: Created page with "=Introduction= Needed to know this for [Rational Zero Theorem] so here goes"

2026-04-20T06:41:56Z

Created page with "=Introduction= Needed to know this for [Rational Zero Theorem] so here goes"

New page

=Introduction=
Needed to know this for [Rational Zero Theorem] so here goes