# AII.1c - Factoring Polynomials

AII.1  The student will

c)  factor polynomials completely in one or two variables.

### BIG IDEAS

• I can design the track of a roller coaster, determine the sloped curve of an exit ramp, trace the free falling path of a skydiver, and understand the mechanics of controllers like autopilot, cruise control, and a living room thermostat.
• I will apply mathematical processes for basic operations to algebraic expressions and divide algebraic terms out of algebraic expressions.

### UNDERSTANDING THE STANDARD

2016 VDOE Curriculum Framework - AII.1 Understanding

·  The complete factorization of polynomials has occurred when each factor is a prime polynomial.

·  Pattern recognition can be used to determine complete factorization of a polynomial.

·  Polynomials may be factored in various ways, including, but not limited to grouping or applying general patterns such as difference of squares, sum and difference of cubes, and perfect square trinomials.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·  AII.1c1  Factor polynomials in one or two variables with no more than four terms completely over the set of integers. Factors of the polynomial should be constant, linear, or quadratic.

·  AII.1c2  Verify polynomial identities including the difference of squares, sum and difference of cubes, and perfect square trinomials.

### KEY VOCABULARY

rational, radical, polynomial expression, simplify, variables, equation vs. expression, factor completely, rational exponents,  sum, difference,product, quotient,monomial, binomial, complex algebraic fraction, simple algebraic fraction, radical expression, radical notation, exponential notation, rationalizing, numerator, denominator, difference of squares, difference of cubes, sum of cubes, perfect square trinomial, integer, verify

Updated: Aug 23, 2018