Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8. 4k^-1+k^-2

Verified step by step guidance

1. Identify the terms in the expression: \$4k^{-1}\( and \)k^{-2}$.
2. Determine the least power of the variable \(k\) in the expression, which is \(k^{-2}\).
3. Factor out \(k^{-2}\) from each term in the expression.
4. Rewrite each term by dividing by the factored out expression: \$4k^{-1} = 4k^{-2} \cdot k\( and \)k^{-2} = k^{-2} \cdot 1$.
5. Express the factored form as \(k^{-2}(4k + 1)\).

Key Concepts

Factoring

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. In algebra, this often involves identifying common terms or expressions that can be extracted from a polynomial or algebraic expression, simplifying the problem and making it easier to solve.

Least Power of a Variable

The least power of a variable in an expression refers to the term with the smallest exponent for that variable. When factoring, identifying the least power allows for the extraction of that term from each part of the expression, simplifying the overall expression and making it easier to manipulate or solve.

Positive Real Numbers

Positive real numbers are all the numbers greater than zero, including both rational and irrational numbers. In the context of algebra, assuming variables represent positive real numbers ensures that operations such as division and taking roots are valid, as they avoid issues with undefined expressions or negative results in certain contexts.