Students solve equations and inequalities involving absolute value. Students are adept at operations on polynomials, including long division. Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes. Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically. In particular, they can plot complex numbers as points in the plane.
Students add, subtract, multiply, and divide complex numbers.
Students add, subtract, multiply, divide, reduce and evaluate rational expressions with monomial and polynomial denominators, and simplify complicated fractions including fractions with negative exponents in the denominator. Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system. Students demonstrate and explain the effect changing a coefficient has on the graph of quadratic functions.