Final answer:
The negative middle number in split factoring indicates a negative coefficient for the bx term in a quadratic equation. Negative exponents result in the reciprocal of the base raised to a positive power.
When dealing with inequalities, multiplying or dividing by a negative number reverses the inequality's direction.
Step-by-step explanation:
When dealing with the split factoring rule in mathematics, if you encounter a middle number that is negative, this implies that when you are factoring a quadratic expression such as ax^2 + bx + c, the term bx will have a negative coefficient. This negative middle term affects the signs of the binomials into which the quadratic is factored.
Simplifying expressions with negative exponents requires understanding that a negative exponent indicates that the base should be placed in the denominator and the exponent made positive. For example, x-n = 1/xn. When multiplying numbers, if they have the same sign, the product is positive, but if they have different signs, the product is negative.
Inequalities also have rules related to negative numbers. Multiplying or dividing both sides of an inequality by a negative number will reverse the inequality sign, demonstrating the importance of carefully considering the sign of numbers in mathematical operations.