Factoring
There are different ways to factor a equation when in standard form because of the equation. There are five different equations when factoring. Factoring a standard form equation is done so you can turn standard form into factored form. This is an important lesson because it easy to graph from factored form. The five ways of factoring are common factoring, simple and complex trinomial factoring and last but not least we have perfect and difference of squares factoring.
Common Factoring
Common Factoring is basically dividing out unnecessary information. But, when you multiply the equation you end up with you will get the same equation. Factoring means dividing and putting it in front of the parentheses. Remember that you are only rearranging the equation nothing disappears.
Here is how you common factor common factoring.
5xy+10y+45x^2+10y^2
this equation would turn into:
5y(x+2+9x^2+2y)
This video was created by my friend and it explains common factoring very well.
Here is how you common factor common factoring.
5xy+10y+45x^2+10y^2
this equation would turn into:
5y(x+2+9x^2+2y)
This video was created by my friend and it explains common factoring very well.
Simple Trinomial Factoring
Factoring a simple trinomial is important when learning how to factor because simple trinomial is used to factor other factoring methods. A simple trinomial is when you have three different terms, but the a value is one, in the standard form equation (y=ax^2+bx+c).
Here is how you factor using a simple trinomial.
To Simple factor a simple trinomial, it's not hard. All you have to do is understand the equation.
x^2-2x-35
to factor you need two brackets, and both brackets need to equal to the equation.
Easy rule to follow is multiply to C and add to B.
x^2 is A
-2x is B
-35 is C
two factors that add to -35 but also multiply to -2.
The factors could be 7 and 5.
-7 and +5 because C is a negative.
The equation would turn into y=(x-7)(+5)
This video was created by my friend and it explains simple trinomial factoring very well.
Here is how you factor using a simple trinomial.
To Simple factor a simple trinomial, it's not hard. All you have to do is understand the equation.
x^2-2x-35
to factor you need two brackets, and both brackets need to equal to the equation.
Easy rule to follow is multiply to C and add to B.
x^2 is A
-2x is B
-35 is C
two factors that add to -35 but also multiply to -2.
The factors could be 7 and 5.
-7 and +5 because C is a negative.
The equation would turn into y=(x-7)(+5)
This video was created by my friend and it explains simple trinomial factoring very well.
Complex Trinomial Factoring
Complex trinomial factoring is used when you have an equation that is in standard form, but the a value in standard form (y=ax^2+bx+c) is higher than one.
This is how you factor complex trinomials.
12x^2-11x+2
This is how you factor complex trinomials.
12x^2-11x+2
- what is c (a*c gives you your c). 12*2=24
- factors of 24: plus or minus 1,2,3,4,6,8,12,24
- factors that will give you b and will satisfy the 2 conditions; 2 factors when added equal b, and when the 2 factors are muliplied give you the c value *(remember the 2 factors have to equal the new c value, 24)*. Therefore the 2 factors that satisfy these conditions are -3 and -8.
- 12x^2-3x-8x+2, now factor by grouping
- 3x(4x-1)-2(4x-1)
- (4x-1)(3x-2)
- Check by expanding and simplifying
- This video was created by my friend and it explains complex trinomial factoring very well.
Perfect Squares Factoring
To factor a perfect square trinomial the first thing you should check is if you can factor the a and the c value in standard form (y=ax^2+bx+c). If you can factor those two terms you can factor a a perfect square. When factoring a perfect square it would look like this: (a+b)^2 which is equal to a^2+ 2ab + b^2.
This is how you would factor a perfect square:
e.g.
4x^2-20xy+25y^2
This is a perfect square because the square of the 1st and 3rd term multiplied by 2 gives you -20xy
This equation would be (2x-5y)^2
This is how you would factor a perfect square:
e.g.
4x^2-20xy+25y^2
This is a perfect square because the square of the 1st and 3rd term multiplied by 2 gives you -20xy
This equation would be (2x-5y)^2
- This video was created by my friend and it explains Perfect Square factoring very well.
Difference of Squares Factoring
To factor a difference of squares it is very similar to perfect square factoring because you only have to change one of the signs. You only have to change one sign from perfect squares. The sign you change is one of the pluses to a minus. That is why the equation becomes (a+b)(a-b) or it will expand to equal a^2 - b^2.
This is how you would factor for a difference of squares:
This is how you would factor for a difference of squares:
- This video was created by my friend and it explains Difference of Square factoring very well.