Algebra 1
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Factorising an Expression
An algebraic factor of a polynomial expression divides evenly into the expression leaving no remainder.
The method of factorising depends on the structure of the polynomial expression.
Highest Common Factor
2x2 + 4x = 2x (x + 2)
Grouping
3x2y + 6xy2 + 5x2 + 10xy
3xy (x + 2y) + 5x (x + 2y)
(3xy + 5x) (x + 2y)
Difference of Two Squares
x2 – y2 = (x + y) (x – y)
Quadratic Trinomial
x2 – 2x – 3 = (x – 3) (x + 1)
Cubic
x3 – y3 = (x – y) (x2 + xy + y2)
x3 + y3 = (x + y) (x2 – xy + y2)