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Given the quadratic trinomial, a, b ,c integers:
(The signs are included in b and c.)
The trinomial will factor with rational factors if:
ax2 + bx + c, a > 0
b2 − 4ac = d2, d > 0
factorable trinomial
a = 4, b = -12 , c = -9
(-12)2 - 4(4)(-9) = 288 ≠ d2
→ not factorable
a = 4, b = -12 , c = 9
b2 − 4ac = 0
(-12)2 - 4(4)(9) = 0 perfect square trinomial
4x2 - 12x + 9 = (2x - 3)2
a = 4, b = 15 , c = 9
(15)2 - 4(4)(9) = 81 = 92
4x(x + 3) + 3(x + 3)
(4x + 3)(x + 3)
