Strategies for factoring.

2 terms

4 terms

3 terms

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Trinomial of the form

Perfect Square trinomial

Difference of square

Sum diffrence of cubes

We use AC method (grouping)

two terms, both terms are perfect cubes and sum of a difference

How to factor: 2d2 + 15d+ 18= 2*18=36,

2d2+12d+3d+18, 2d(d+6) +3(d+6)= (2d+3) (d]+6)

Examples x3 + 8= (x+2)(x2-2x+4)

8a3-216b3= 8(a3-27b3) GCF (a-3b) (a2-3ab+9b2)

How to factor: x2 + 12x + 36= 2(6)(x), (x+6)2

3 terms ( write descending order), the 3rd term is always positive, the 1st term and the 3rd term are perfect squares.

Factor by Grouping

Common Polynomial Factor

Common Monomial Factor

Two terms each is a perfect square

x2-64(x-8)(x+8)

We have to found the GCF of all terms

We have to put together both parentesis that are the same and in an other parentesis the other two parentesis. Then we simplificate the second parentesis.

1/4x6-9/25x4 (1/2x3-3/5x2)(1/2x3+3/5x2)

9y4 - 15y3 +3y2 = 3y2 (3y2 - 5y+ 1)

(a-b) + (x+5) (a-b) (x-y2) = (a-b) (x+5+x-y2) = (a-b) (2x+5-y2)

Look 2 numbers that you can multiplied give you "C" and added or substracted is "b".

1.- Group terms in pairs 2.- Find BCF 3.- Froup polynomial factors.

y3 +3y2+4y+12 = y2 (y+3) +4 (y+3) = (y+3) (y2+4)

How to factor: x2 - 7x + 12= (x - 4)(x - 3)

Trinomial

x2-3x+18 (x-6)(x+6)

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

6x2y-21x3y2+3x2y3= 3x2y(2-7xy+1y2)

2nd Example: y2 -10y + 25= (y - 5)2

12t5 -20t4 + 8t2 - 16= 4(3t5-5t4+2t2-4)