How to Factor Polynomials - Revision history

Iwiseman at 01:04, 21 April 2026

2026-04-21T01:04:31Z

@@ Line 9: / Line 9: @@
 x² + 8x = 4x(x+2) GCF = 4x
 x² -15x³ = 5x²(1 -3x) GCF = 5x²
 =Factoring by Trinomials=
 For these you look for numbers which multiply to the constant and add up to the coefficient of the x term

Iwiseman at 01:01, 21 April 2026

2026-04-21T01:01:38Z

← Older revision		Revision as of 01:01, 21 April 2026
Line 1:		Line 1:
	=Introduction=		=Introduction=
	I have another page on this, which listed 10 approaches to factoring. I stopped it at #9 Long Division because it said I must understand [[Factor Theorem]] and [[Rational Zero Theorem]] which I did not. This led me in the end to here https://www.video-tutor.net/polynomials.html and why this exists on my wiki		I have another page on this, which listed 10 approaches to factoring. I stopped it at #9 Long Division because it said I must understand [[Factor Theorem]] and [[Rational Zero Theorem]] which I did not. This led me in the end to here https://www.video-tutor.net/polynomials.html and why this exists on my wiki
			=Greatest Common Factor (GCF)=
			This is where you look at a polynomial and find, you guest it, the greatest common factor so given
			3x + 15
			It would be 3 because
			3(x + 5)
			And
			4x² + 8x = 4x(x+2) GCF = 4x
			5x² -15x³ = 5x²(1 -3x) GCF = 5x²
			=Factoring by Trinomials=
			For these you look for numbers which multiply to the constant and add up to the coefficient of the x term
			x² + 3x - 28
			So in the case two numbers which multiply to -28 and add up to +3<br>
			<br>
			So 28 factors are 1, 28, 2, 14, 7, 4 - so 7 and 4
			(x -4)(x+7)
			And given
			x² - 3x - 10
			So factors of 10 are 1,10,2,5 - so 5 and 2
			(x-5)(x+2)
			When the first term is not x² for example
			2x² + 20x + 48
			Just get rid of the 2
			2(x² + 10x + 24)
			2(x+4)(x+6)
			What do you do I you cannot factor out to x². A tiny bit more complex this bit because the slight of hand of the youtuber. You need to multiply the coefficient of the first term with the constant and then look for two numbers which when added together = the middle term. So given
			2x² - 5x + -3
			So 2x -3 = -6 and factors of -6 are 2, -3, 1 -6<br>
			So 1 -6 = -5 = the middle term coefficient<br
			And this was the tricky bit. Just replace p-5x with -6x +1x. It is obvious when you see it but they mean replace the middle term with the factors you identified. In this case 1 and -6. So we have
			2x² - 6x + 1x -3
			So using the grouping approach take out the GCF we have
			2x(x-3) + 1(x-3)
			(x-3)(2x+1)

Iwiseman: /* Introduction */

2026-04-21T00:59:47Z

Introduction

← Older revision		Revision as of 00:59, 21 April 2026
Line 1:		Line 1:
	=Introduction=		=Introduction=
	I have another page on this, which listed 10 approaches to factoring. I stopped it at #9 Long Division because it said I must understand [[Factor Theorem]] and Rational Zero Theorem]] which I did not. This led me in the end to here https://www.video-tutor.net/polynomials.html and why this exists on my wiki		I have another page on this, which listed 10 approaches to factoring. I stopped it at #9 Long Division because it said I must understand [[Factor Theorem]] and [[Rational Zero Theorem]] which I did not. This led me in the end to here https://www.video-tutor.net/polynomials.html and why this exists on my wiki

Iwiseman: Created page with "=Introduction= I have another page on this, which listed 10 approaches to factoring. I stopped it at #9 Long Division because it said I must understand Factor Theorem and Rational Zero Theorem]] which I did not. This led me in the end to here https://www.video-tutor.net/polynomials.html and why this exists on my wiki"

2026-04-21T00:59:27Z

Created page with "=Introduction= I have another page on this, which listed 10 approaches to factoring. I stopped it at #9 Long Division because it said I must understand Factor Theorem and Rational Zero Theorem]] which I did not. This led me in the end to here https://www.video-tutor.net/polynomials.html and why this exists on my wiki"

New page

=Introduction=
I have another page on this, which listed 10 approaches to factoring. I stopped it at #9 Long Division because it said I must understand [[Factor Theorem]] and Rational Zero Theorem]] which I did not. This led me in the end to here https://www.video-tutor.net/polynomials.html and why this exists on my wiki