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.

## Comments

^{2}- 23x + 21] and then you just multiply each term in the parentheses by 2 to get 12x^{2}- 46x + 42.