Guidelines for Factoring!
1. Put in polynomial in descending order.
a. ( Ex. 5x + 6 + x2 = x2 + 5x + 6 )
b. Except when a difference of squares, leave as is.
i. ( Ex. 16 - x2 )
2. Factor out a GCF where possible.
a. ( Ex. 2x2 + 10x + 12 = 2(x2 + 5x + 6) )
3. If x2 + bx + c use a Product/Sum Table.
Product 6 Sum
a. x2 + 5x +6
2x3
5
(x + 2)(x + 3)
4. If ax2 + bx + c use decomposition, or the box method
a. 3x2 + 8x + 4
Product 3 x 4 = Sum
2
3x +6x + 2x + 4
12
3x(x+2) + 2(x + 2) 6 x 2
8
(3x + 2)(x + 2)
b. Be aware of perfect square trimonials:
i. a2 +2ab +b2 = (a + b)2
ii. Ex. 121a2 + 110a +25
(11a + 5)(11a + 5) = (11a + 5)2
5. If a difference of squares leave order as is and factor using
pattern
a. a2 – b2 = (a - b)(a + b)
i. Ex. 16 – x2 = (4 – x)(4 +x)