Strategies of Factoring

Andre Alarcon and Carlos Parra

2 Terms

Difference of square

Difference of cubes

3 terms

-Two terms (each one is a perfect square)
-Diference
HOW TO FACTOR
a²-b²=(a+b)(a-b)

Perfect Square Trinomial

Trinomial of the Form

Trinomial of th form where a is 1

3 terms. 3rd term is always positive. 1st and 3rd squares are perfect squares

Characteristics

EXAMPLES
a) x²-64=(x-8)(x+8)
b)12x²-75=3(4x²-25)=3(2x-5)(2x+5)

Examples

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-Two terms
-Both termsare perfect cubes
-Sum or a diference
HOW TO FACTOR
a3+b3=(a+b)(a2-ab+b2)

The numbers of the parentesis multiplicated give the number on the center

3 terms We need to search for 2 numbers that multiplicated give the 3rd number and added the 2nd

m²+10x+21
(m+3)(m+7)

a²-11ab-60b²
(a+15b)(a-4b)

Whe have 4 terms.And we need to search what the 1rst and 2nd numbers have in common and what 3rd and 4rth number have in common.

2d²+12d+3d+18
2d(d+6)+3(d+6)

EXAMPLES
x3+8=(x+2)(x2+2x+4)
64x3+27y3=(4x+3y)(16x2-12xy+9y2)

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We have to search a number that they have in common

4 Terms

Grouping

Comon monomial factor (first step)

THE FISRST THING THAT YOU NEED TO DO IS TO SEE THE GCF

Common Polinomial Factor (second step)

To solve in this form you need to take the gcf fiirst

When we have 2 paraentesis whit the same thinks we do CPF (Common Polinomial Factor) to solve it

12a3-9a2+4a-3=3a2(4a-3)+1(4a-3)=

m3-m2+2m-2=m2(m-1)+2(m-1)=

EXAMPLE

Characteristics

Example

3a²(4a-3)+1(4a-3)
(3a²+1)(4a-3)

M²(M-1)+2(M-1)
(M²+2)(M-1)

Andre Alarcon and Carlos Parra

Andre Alarcon

a² +2a+1 (a+1)² 16c²+72cd+81d² (4c+9d)²

And when we have the parentesis whit the same number we only get down the parentesis and the numbers that are outside

Characteristics