Students are able to find the equation of a line perpendicular to a given line that passes through a given point. Students solve a system of two linear equations in two variables algebraically, and are able to interpret the answer graphically. Students are able to use this to solve a system of two linear inequalities in two variables, and to sketch the solution sets. Students add, subtract, multiply and divide monomials and polynomials. Students solve multistep problems, including word problems, using these techniques.
Students apply basic factoring techniques to second and simple third degree polynomials.
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.