These techniques include finding a common factor to all of the terms in a polynomial and recognizing the difference of two squares, and recognizing perfect squares of binomials. Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing to lowest terms. Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems using these techniques. Students solve a quadratic equation by factoring or completing the square.
Students apply algebraic techniques to rate problems, work problems, and percent mixture problems.
Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions. Students determine the domain of independent variables, and range of dependent variables defined by a graph, a set of ordered pairs, or symbolic expression. Students determine whether a relation defined by a graph, a set of ordered pairs, or symbolic expression is a function and justify the conclusion. Students know the quadratic formula and are familiar with its proof by completing the square. Students use the quadratic formula to find the roots of a second degree polynomial and to solve quadratic equations.