Question 326194
subtracting 42+9x ___ 2x^2 - 8x - 42 = 0


the factors of 2x^2 are 2x and x


the factors of -42 are (±1, ±42), (±2, ±21), (±3, ±14), (±6, ±7)


you need to "combine" the 2x and x with one of the other pairs of factors to end up with -8x
___ the "combining" is summing the products of the pairs by FOILing


2x times 3 is 6x ___ x times -14 is -14x ___ this gives you the -8x


so the factors are ___ (2x - 14) and (x + 3) ___ (2x - 14)(x + 3) = 0


the zero principle means that any (or all) of the quantities, whose product is zero, must be zero


2x - 14 = 0 ___ 2x = 14 ___ x = 7


x + 3 = 0 ___ x = -3