I just need help factoring quadratic trinomials. Specifically 12x2 + -46x + 42.
12 X^{2} - 46X + 42 = 2 ( 6X^{2 }- 23X + 21)
two factor : Must be 2 numbers a,b such that a . b = 6 ( 21) = 126 a+b =-23
first we write 126 as a product of its prime factors:
126 = 2 . 3 . 3 . 7 = 2 * 63 = 6 * 21= 18 * 7 = 14 * 9
We find that: -14 - 9 = -23
break up -23 into -14 - 9 = -23
2( 6 X^{2} - 9X - 14 X + 21) = 2 [ 3X( 2X -3) - 7( 2X -3) ] = 2( 2X -3 ) ( 3X -7 )
This is the methods by which step by step can be followed to get the result, be able to factor.
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