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Binomial expressions are algebraic expressions that contain two distinct terms. An example of a binomial expression is \((h + 5)\). The word 'binomial' comes from the Latin 'bi-' meaning two and 'nomial' referring to terms, so it literally means having two terms. As seen in mathematics, binomials are often found in equations and inequalities, where they need to be manipulated or solved. The expression \((h + 5)^2\) given in the inequality is a square of a binomial, which expands to \(h^2 + 10h + 25\).
Squaring creates a nonnegative result because any number, whether positive or negative, becomes positive when squared. This characteristic is crucial in understanding why the inequality \((h + 5)^2 \geq -2\) holds true for all real numbers. Understanding binomials and their properties helps in quickly identifying that a squared binomial results in a non-negative quantity.

Real numbers encompass all numbers that can be found on the number line. This includes all rational numbers (like integers and fractions) and irrational numbers (like the square root of 2 or \(\pi\)). Real numbers can be positive, negative, or zero, and they are the foundation of many mathematical concepts and solutions.
In the context of the given inequality \((h + 5)^2 \geq -2\), we determine that for all real numbers \(h\), the inequality is satisfied because any squared number is non-negative. Thus, this provides a solution that spans the entire set of real numbers.
Being fluent with real numbers allows for a comprehensive understanding of inequalities and solutions in algebra, helping you interpret the results effectively across different problem sets.

Interval notation is a mathematical concept used to express a range of values succinctly. It is particularly useful in inequalities to show the set of all possible solutions. This notation uses parentheses \(()\) and brackets \([]\). Parentheses indicate that an endpoint is not included, while brackets indicate inclusion.
When discussing the solution to the inequality \((h + 5)^2 \geq -2\), we find that all real numbers are solutions. In interval notation, this is expressed as \((−\infty, +\infty)\). This notation efficiently communicates that every real number from negative infinity to positive infinity satisfies the inequality.
By mastering interval notation, you can clearly and effectively write solutions for a variety of algebraic problems, ensuring your solutions are easily understood by others.