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Factoring Special Quadratic Polynomials
WHAT TO DO:
HOW TO DO IT:
If there is no common factor check for the two
special types of factorable polynomials:
(a) difference of squares
The difference of squares always factors to the sum and
difference of the square roots of those squares.
A2 − B2
= (A + B)(A − B)
a) Factor 4x2 − 9 difference of squares (binomial)
a) 4x2
− 9 = (2x + 3)(2x − 3)
b) Factor 9x2 − 25 difference of squares (binomial)
b) 9x2
− 25 = (3x + 5)(3x − 5)
b) perfect square trinomial
Perfect square trinomials must have the first and last
terms be perfect squares and the last sign positive. If
all of these conditions hold, check to see if the product
of the square roots of the first term and the last term
is the same as half the middle term or
if the middle term is twice the cross product of the
square roots.
The “middle signâ€
is the “sign of the binomialâ€.
→ Factor the trinomial: 25x2 + 60x + 36
= (5x + 6)2
NOTE: If the trinomial isn’t immediately recognized as a perfect square trinomial,
the best method is to treat it as “any trinomial†and use factor by grouping.
