y + 5x = 6 if x = {-1, 0, 1}
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4x2+3x+6+5x+3x+6 = 4x2+11x+12 when simplified
-4x2 + 5x + 6 = 0 Multiply through by -1: 4x2 - 5x - 6 = 0 (I prefer the leading coefficient to be >0) 4x2 - 8x + 3x - 6 = 0 4x(x - 2) + 3(x - 2) = 0 (x - 2)(4x + 3) = 0 So x - 2 = 0 or 4x + 3 = 0 ie x = 2 or x = -3/4
Reading this as: 4x2-6=2x2 This implies that: -6=-2x2 3=x2 x=sqrt(3) and x=-sqrt(3) So x can equal plus or minus the square root of 3
Divide all terms by 4:- x2+5x-6 = (x-1)(x+6) when factored
x3 - 4x2 + x + 6 The sum of the odd coefficients equals the sum of the even coefficients, so (x + 1) is a factor. So x3 - 4x2 + x + 6 = x3 + x2 - 5x2 - 5x + 6x + 6 = x2(x + 1) - 5x(x + 1) + 6(x + 1) = (x + 1)(x2 - 5x + 6) = (x + 1)(x - 2)(x - 3)