What values of x make the expression (x+7)(x-10) negative?

Answer 1

An easy way to do this is by graphing on a calculator. First, write the polynomial that you get when you expand the expression. In other words, use F.O.I.L. on (x+7)(x-10) to get x²-10x+7x-70--->x²-3x-70. Graph this and you see that you have a parabola that opens up and crosses the x-axis at x=-7 and x=10. All the y values are negative when x is between, but not including, -7 and +10. So, your answer is -7<x<10.