SOLUTION: factor completely 16x^2-2x-3

Question 93562: factor completely
16x^2-2x-3
Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
DEFINE ALL FACTORS OF 16=1,-1,2,-2,4,-4,8,-8,16&-16
DEFINE ALL FACTORS OF -3=1,-1,3&-3
NOW FIND ONE SET OF FACTORS THAT WHEN MULTIPLIED AND THEN ADDED=(-2).
PICK ONE FACTOR FROM 16 & ONE FROM -3 MULTIPLY THESE FACTORS. NOW MULTIPLY THE COMPANION FACTOR OF 16 & -3. MULTIPLY THESE FACTORS. NOW ADD THESE TWO PRODUCTS. THEY SHOULD EQUAL -2.
THERE IS ONLY ONE SET OF FACTORS THAT SATISFY THIS PROBLEM.
8*-1=-8 & 2*3=6 [8*2=16 & -1*3=3] THEN -8+6=-2 WHICH IS THE MIDDLE TERM.
6x^2-2x-3
(8x+3)(2x-1)
THIS LOOKS COMPLICATED BUT WITH A LITTLE PRACTICE YOU CAN MASTER IT. "DON'T GIVE UP THE SHIP JUST BECAUSE THERE IS A WHITE CAP ON THE HORIZEN".
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