#### Math - 2017-18

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

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

d) **factor **polynomials
completely.

AII.1The student willc)

factorpolynomials completely in one or two variables.

**Bloom's Level:** Evaluate

*Adopted: 2009*

### 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.
- Only radicals with a common radicand and index
can be added or subtracted.
- 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.1d_{1} **Factor** polynomials by applying general
patterns including difference of squares, sum and difference of cubes, and
perfect square trinomials.

All.1d_{2} **Factor** polynomials completely over the
integers.

·
AII.1c_{1} **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.1d_{3} **Verify**
polynomial identities: difference of squares, sum and difference of cubes, and
perfect square trinomials.

·
AII.1c_{2} **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*