FACTORING WHEN a=1

What does it mean to factor? To factor is to UNDO multiplication Before we multiplied (x+1)(x+4) to get x2+5x+4 Now we are going to factor x2+5x+4 to get (x+1)(x+4) (x+1) and (x+4) are called factors

Figuring out the Factors You want 2 numbers that multiply to give you c AND add to give you b?

x2 +7x + 6 x2 +7x + 6 ( )( ) x x + 6 + 1

x2 + 9x + 14 x2 + 9x + 14 ( )( ) x x + 7 + 2

x2 – 6x + 8 x2 – 6x + 8 ( )( ) x x – 4 – 2

x2 – 10x + 16 x2 – 10x + 16 ( )( ) x x – 8 – 2

Sign Rule: When C is POSITIVE… The signs of both factors will be the SAME as the sign of b

Sometimes you can factor out a GCF first Sometimes you can factor out a GCF first! Look for something all terms have in common

2x2 – 16x + 24 2(x2 – 8x +12) 2( )( ) x x – 6 – 2

n2 + 2n – 48 ( )( ) n n + 8 – 6

x2 + 8x – 20 ( )( ) x x – 2 + 10

x2 – 4x – 21 ( )( ) x x + 3 – 7

x2 – 9x – 36 ( )( ) x x + 3 – 12

Sign Rule: When c is NEGATIVE… The factors will have DIFFERENT SIGNS. The larger factor will have the SAME sign as b

Sometimes there is no middle term! That means b=0!

x2 - 16 x2 + 0x - 16 ( )( ) x x + 4 – 4