Question

What values of x make the (x-3)(x+5) expression negative ?

Answer 1

The expression (x-3)(x+5) is negative when x is greater than -5 and less than 3, meaning the answer is for the range -5 < x < 3.

Step-by-step explanation:

To find the values of x that make the expression (x-3)(x+5) negative, we need to consider the individual factors within the expression. An expression is negative if one factor is positive and the other is negative. Therefore, we need to evaluate the sign of each factor separately over different intervals of x.

Let's consider the two factors, x-3 and x+5:

• First factor (x-3): This factor is positive when x > 3 and negative when x < 3.
• Second factor (x+5): This factor is positive when x > -5 and negative when x < -5.

Now, let's combine these intervals to determine when their product is negative:

• When x < -5, both factors x-3 and x+5 are negative, so their product is positive.
• When -5 < x < 3, the factor x-3 is negative and x+5 is positive, thus their product is negative.
• When x > 3, both factors are positive, and so their product is positive.

Therefore, the expression (x-3)(x+5) is negative when x is between -5 and 3.