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WHAT TO DO:
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HOW TO DO IT:
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| 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 |
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perfect square trinomial factorable trinomial |
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| a) Test 4x2 - 12x - 9
a = 4, b = -12 , c = -9 |
4x2 - 12x - 9
(-12)2 - 4(4)(-9) = 288 ≠ d2
→ not factorable |
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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 |
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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.
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4x2 + 12x + 3x+ 9
4x(x + 3) + 3(x + 3)
(4x + 3)(x + 3) |
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4x2 + 15x + 9 = (4x + 3)( x + 3) |
