​Quadratic Relationships

In factoring you have, common, simple trinomial, complex trinomial, perfect square and diffrence of squares. 

 

For common factoring, all you need to do is write an expression using things that we could multiply to make that expression.

For example, 3x + 6 factors into 3 ( x +2 )

 

Next you have Simple trinomial, for this you just make the coefficent of the "a" value 1. 

For example, x2 + 7x + 12 factors into ( x + 3) ( x + 4) because x multiplied by x is x2 and x multiplied by 4 is 4x and then 3 multiplied by x is 3x and then 3 multipled by 4 is 12. So in the end it would look like x2 + 7x + 12. Tip : choose two numbers that would multiply to the c value and add up to the b value.

 

Now you have complex trinomial. The diffrence between a complex and simple is that now x2 has a coefficent other than 1. So to factor complex trinomials you would use the methos guess and check.

For example, 3x2 + 13x + 12 factors into ( x + 3) ( 3x + 4).

Now we check: 

 ( x + 3) ( 3x + 4)

= 3x2 + 4x + 9x + 12

= 3x2 + 13x + 12

So it works !

 

Perfect Squares, for this it basically starts and ends with a square. 

For example, 4x2 + 12x + 9 factors to ( 2x + 3) ( 2x + 3) and as a perfect square ( 2x+ 3 )2.

NOTE: A perfect square trinomial always starts and ends with a square and looks like : a + b2 = a2 + 2ab + b2

 

Finally Diffrence of Squares, it is basically where the middle terms cancel out & has same values & diffrent signs. For example, x2-9 is x2 + 0x - 9 as a trinomial and it factors to (x-3) (x+3)

NOTE: A trinomial is a diffrence of squares if it looks like this: a2-b2 = (a + b) (a - b)