Directions: Use only the digits 1-9, each digit only once, create a problem that has the solutions x = 4 and x = -1/2.

### Hint

If you were to solve this equation, what would your first step be?

How does the Zero Product Property help us rewrite this equation?

What would the parameters need to be in the first factor to result in a solution of x = 4?

### Answer

If (ax + b)(cx + d) = 0, there are infinite answers of the form -b/a = 4 and -d/c = -1/2.

Most commonly found student answer: (1x + -4)(2x + 1) = 0.

Source: Amy Herzog

I like this question but if we can only use the digits 1-9, how can we end up with 1x+ (-4) as one of the factors?

And 1 is used twice…

I am going to change the first sign to a – and then it will work.

(_x-_)(_x+_) and a possible answer would be (1x-4)(6x+3)