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Factoring Polynomials, hint: negative "ac" means think…
Factoring Polynomials
Special challenges
Many Variables
pattern: x^2 xy y^2
(x y)(x Y)
use usual trinomial strategies
common factor
Difference of squares?
Higher powers
Pattern: bigger power twice the size of smaller
x^4 + 2 x^2 + 1 = (x^2 +1) (x^2 +1)
treat like normal
common factors
group terms
might not work
Goal: get two brackets that are the same OR something that can be further factored
factor smaller groups
brackets
can be common factors
can be thought of as variables
Algebra Tiles
tile values
small square = 1
long rectangle= x
big square= x^2
negatives are a different colour
x
filling a rectangle
put tiles along each edge
draw lines down and across to fill in
/ aka factoring
arrange tiles into rectangle in middle
how long are each side?
Difference of Squares
TWO perfect squares
1
higher powers: x^4, x^6 (even power)
many variables
SUBTRACTION
Pattern: ( + )( - )
fill with roots of squares
Trinomials a not 1
common factor
factors can be larger
ex: (x+3)
Regrouping
a x c
look for two numbers
multiply = ac
add = b
split middle term into two
common factor from 1st two terms
then from last two
factor out common bracket
if not the same
error
factor our a negative
Trinomials a=1
x^2 + 7x + 12 (x+3)(x+4)
multiply to c, add to b
put into two brackets
Common Factor
hint: negative "ac" means
think subtraction