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Factoring
• The process of finding polynomials whose
product equals a given polynomial is
called factoring.
• Prime polynomial: A polynomial with
variable terms that cannot be written as a
product of two polynomials of lower
degree.
Factoring Out the Greatest Common Factor
Factoring by Grouping
When a polynomial has more than three terms, it
can sometimes be factored by grouping.
Factoring Trinomials
Factoring trinomials requires using the FOIL
method in reverse.
To factor ax^{2} + bx + c we find integers a_{1}, a_{2}, c_{1},
and c_{2} such that:
where a_{1} and a_{2} are factors of a, and c_{1} and c_{2} are
factors of c.
Perfect Square Trinomials
Factoring Special Binomials
Difference of Squares: x^{2}  y^{2} = (x + y)(x  y)
Sum of Cubes: x^{3} + y^{3} = (x + y)(x^{2}  xy + y^{3})
Difference of Cubes: x^{3} + y^{3} = (x  y)(x^{2} + xy + y^{3})
Check by multiplying.
Check by multiplying.