Question

What are the solutions to the equation (x – 2)(x + 5) = 0?

Answer 1

your Answer:

C: x = 2, -5

Answer 2

A product of two (or more) factor can be zero if and only if at least one of the factors is zero.

In other words, you cannot multiply two non-zero real numbers, and have zero as a result.

So, if we want the product of these two factors to be zero, at least one of them has to be zero.

The first factor is zero if

$x-2 = 0 \iff x=2$

The second factor is zero if

$x+5 = 0 \iff x=-5$