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# Test for Factorability for Quadratic Trinomials

 WHAT TO DO: HOW TO DO IT: The test for factorability is relatively simple but it requires one to have a knowledge of the squares of integers or access to a calculator. Given the quadratic trinomial, a, b ,c integers: (The signs are included in b and c.) The trinomial will factor with rational factors if: Review squares of integers. ax2 + bx + c, a > 0 b2 − 4ac = d2, d > 0 perfect square trinomialfactorable trinomial a) Test 4x2 - 12x - 9 a = 4, b = -12 , c = -9 4x2 - 12x - 9 (-12)2 - 4(4)(-9) = 288 ≠ d2 → not factorable b) Test 4x2 - 12x + 9 a = 4, b = -12 , c = 9 b2 − 4ac = 0 4x2 - 12x + 9 (-12)2 - 4(4)(9) = 0 perfect square trinomial 4x2 - 12x + 9 = (2x - 3)2 c) Test 4x2 + 15x + 9 a = 4, b = 15 , c = 9 4x2 + 15x + 9 (15)2 - 4(4)(9) = 81 = 92 Find the GN = 36 with factors 3, 12 and sum 15. 4x2 + 12x + 3x+ 9 4x(x + 3) + 3(x + 3) (4x + 3)(x + 3) 4x2 + 15x + 9 = (4x + 3)( x + 3)