Factor each polynomial over the set of rational number coefficients. 49x^2-1/25

Key Concepts

Factoring Polynomials

Factoring polynomials involves expressing a polynomial as a product of its simpler components, or factors. This process is essential for simplifying expressions, solving equations, and analyzing polynomial behavior. Common techniques include identifying common factors, using special product formulas, and applying methods like grouping or the quadratic formula.

Difference of Squares

The difference of squares is a specific factoring pattern that applies to expressions in the form a^2 - b^2, which can be factored into (a - b)(a + b). In the given polynomial, 49x^2 - 1/25, recognizing it as a difference of squares allows for straightforward factoring, where a = 7x and b = 1/5.

Rational Coefficients

Rational coefficients are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. When factoring polynomials over the set of rational numbers, it is important to ensure that all coefficients in the resulting factors are rational. This requirement influences the choice of factoring techniques and the form of the final expression.