Question

How do you use the zero product property to solve `(x-5)(2x+7)(3x-4)=0`?

Answer 1

By the zero product property, you know that the multiplication of several factors is zero if and only if at least one of the factors is zero.

So, your expression is equal to zero if and only if one of the three factors equals to zero. Let's study them separately:

• `x-5=0` if and only if `x=5`
• `2x+7=0` if and only if `x=-\frac{7}{2}`
• `3x-4=0` if and only if `x=\frac{4}{3}`

So, we conclude that `(x−5)(2x+7)(3x−4)=0` if and only if `x` assumes one of the following values: `5, -\frac{7}{2}, \frac{4}{3}`