Strategies for factoring. - Coggle Diagram
Strategies for factoring.
Difference of square
Two terms each is a perfect square
Sum diffrence of cubes
two terms, both terms are perfect cubes and sum of a difference
Examples x3 + 8= (x+2)(x2-2x+4)
8a3-216b3= 8(a3-27b3) GCF (a-3b) (a2-3ab+9b2)
Factor by Grouping
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)
12t5 -20t4 + 8t2 - 16= 4(3t5-5t4+2t2-4)
Common Polynomial Factor
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.
(a-b) + (x+5) (a-b) (x-y2) = (a-b) (x+5+x-y2) = (a-b) (2x+5-y2)
12a3-9a2+4a-3= 12a3-9a2+4a-3 3a2(4a-3) (3a2-1)(4a-3)
Common Monomial Factor
We have to found the GCF of all terms
9y4 - 15y3 +3y2 = 3y2 (3y2 - 5y+ 1)
Trinomial of the form
We use AC method (grouping)
How to factor: 2d2 + 15d+ 18= 2*18=36,
2d2+12d+3d+18, 2d(d+6) +3(d+6)= (2d+3) (d]+6)
Perfect Square trinomial
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.
2nd Example: y2 -10y + 25= (y - 5)2
Look 2 numbers that you can multiplied give you "C" and added or substracted is "b".
How to factor: x2 - 7x + 12= (x - 4)(x - 3)