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Q: How do you factor 6x2 plus 23x plus 7?

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Are those x's or multiplication signs?

I'll assume that that should read: 6x2 + 2x - 28 Then: First take out a common factor of 2: 6x2 + 2x - 28 = 2(3x2 + x - 14) The coefficient of the x2 is 3 and can only be factored as 3 x 1 (and 1 x 3) which means that 3x must be in one factor and x in the other. The other element of each factor is a factor of -14 which can be factorised as: -1 x 14, -2 x 7, -7 x 2 & -14 x 1. Need three times one factor plus the other factor = +1 (the coefficient of the x) Inspection shows that (3 x -2) + 7 = -6 + 7 = 1 works; so put the factor multiplied by 3 with the x and the other factor with the 3x, giving: 2(3x2 + x - 14) = 2(3x + 7)(x - 2)

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