# AII.1d and *AII.1c - Factoring Polynomials

AII.1    The student, given rational, radical, or polynomial expressions, will

d)  factor polynomials completely.

AII.1  The student will

c)  factor polynomials completely in one or two variables.

Bloom's Level:  Evaluate

### 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

• Computational skills applicable to numerical fractions also apply to rational expressions involving variables.
• Radical expressions can be written and simplified using rational exponents.
• A relationship exists among arithmetic complex fractions, algebraic complex fractions, and rational numbers.
• 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.

·  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

Greatest Common Factor

Trinomials (a=1)

Trinomials (a>1)

Binomials (squares, cubes)

All.1d1  Factor polynomials by applying general patterns including difference of squares, sum and difference of cubes, and perfect square trinomials.

All.1d2  Factor polynomials completely over the integers.

·  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.

All.1d3  Verify polynomial identities: difference of squares, sum and difference of cubes, and perfect square trinomials.

·  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: Oct 27, 2017