Which is the integer root of the function f(x) = (2x + 4)(3x − 1)?

The integer root of this function is -2: Here's how you can solve.

Set each binomial equal to zero and solve:
2x + 4 = 0 subtract 4 from both sides
2x = -4 divide both sides by 2
x = -2

Setting the other binomial equal to 0 yields a fractional root.. try for yourself :-)