Louisiana Administrative Code
Title 28 - EDUCATION
Part CLXXI - Bulletin 745-Louisiana Teaching Authorizations of School Personnel
Chapter 23 - Algebra II
Section CLXXI-2303 - Algebra

A. Use the structure of an expression to identify ways to rewrite it.

Example: See x4 - y4 as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).

B. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

C. Apply the formula for the sum of a finite geometric series (when the common ratio is not 1) to solve problems.

Example: Calculate mortgage payments.

D. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a)=0 if and only if (x - a) is a factor of p(x).

E. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

F. Use polynomial identities to describe numerical relationships.

Example: The polynomial identity (x2 + y2)2=(x2 - y2)2 + (2xy)2 can be used to generate Pythagorean triples.

G. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

H. Create equations and inequalities in one variable and use them to solve problems. (Include equations arising from linear and quadratic functions, and simple rational and exponential functions.)

I. Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

J. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

K. Solve quadratic equations in one variable.

L. Solve systems of linear equations exactly and approximately (e.g., with graphs), limited to systems of at most three equations and three variables. With graphic solutions, systems are limited to two variables.

M. Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

Example: Find the points of intersection between the line y=-3x and the circle x2 + y2=3.

N. Explain why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x)=g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.