## Standards of Learning (SOL)

 Essential Knowledge and Skills

• Model sums, differences, products, and quotients of polynomials with concrete objects and their related pictorial and symbolic representations. (b)
• Determine sums and differences of polynomials. (b)
• Determine products of polynomials.  The factors should be limited to five or fewer terms (i.e., (4+ 2)(3+ 5) represents four terms and
(+ 1)(2x2  + 3) represents five terms). (b)
• Determine the quotient of polynomials, using a monomial or binomial divisor, or a completely factored divisor. (b)
• Factor completely first- and second-degree polynomials in one variable with integral coefficients. After factoring out the greatest common factor (GCF), leading coefficients should have no more than four factors. (c)
• Factor and verify algebraic factorizations of polynomials with a graphing utility. (c)

## Resources

Vocabulary
Polynomials, exponent, base, power, law of exponents, operations, factoring, binomial, trinomial, one variable, first-degree, second-degree, simplify, ratios, integers, model, concrete objects, product, difference, sum, quotient, binomial divisor, divisor, coefficient, leading coefficient, factorization, prime polynomials, scientific notation

## Vertical Articulation

Post Standard of Learning

AII.3            The student will solve absolute value linear equations and inequalities; quadratic equations over the set of complex numbers; equations containing rational algebraic expressions; and equations containing radical expressions.

AII.3            The student will solve

a)   absolute value linear equations and inequalities;

b)   quadratic equations over the set of complex numbers;

c)   equations containing rational algebraic expressions; and

 The student will investigate the passage of time and a) tell time to the hour and half-hour, using analog and digital clocks; and b) read and interpret a calendar.
 The student will investigate the passage of time and a) tell time to the hour and half-hour, using analog and digital clocks; and b) read and interpret a calendar.
 The student will investigate the passage of time and a) tell time to the hour and half-hour, using analog and digital clocks; and b) read and interpret a calendar.

## Essential Questions

• Can two algebraic expressions that appear to be different be equivalent?
• How do you add, subtract, and multiply polynomials?
• How can we use the polynomial operations addition, subtraction, and multiplication in practical situations?
• How can you model sums and differences of polynomials with concrete objects, pictures, and symbols?
• How can you model products and quotients of polynomials  with concrete objects , pictures, and symbols?
• How can you determine sums and differences of polynomials?
• How can you determine products of polynomials?
• How can you determine the quotient of polynomials?
• Why do we factor polynomials?
• How do you determine if an expression has a greatest common factor?
• What models can you use to factor first and second degree polynomials?
• How do you factor completely first- and second-degree polynomials in one variable?
• How can we identify a difference of squares?
• What is the relationship between the factor of a polynomial and the graph of the polynomial?
• How can you verify factors of a polynomial with a graph?