#### Math - 2017-18

# A.2c and *A.2c - Factoring Polynomials

**A.2** The student will **perform** operations on
polynomials, including

c) **factoring**
completely first- and second-degree binomials and trinomials in one or two
variables. Graphing calculators will be used as a tool for factoring and for
confirming algebraic factorizations.

A.2The student willperformoperations on polynomials, includingc) factoring completely first- and second-degree binomials and trinomials in one variable.

**Bloom's Level:** Analyze

*Adopted: 2009*

### BIG IDEAS

- I can design the track of a
roller coaster, determine the sloped curve of an exit ramp, 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

- The laws of exponents can be investigated using
inductive reasoning.
- A relationship exists between the laws of
exponents and scientific notation.
- Operations with polynomials can be represented
concretely, pictorially, and symbolically.
- Polynomial expressions can be used to model
real-world situations.
- The distributive property is the unifying
concept for polynomial operations.
- Factoring reverses polynomial multiplication.
- Some polynomials are prime polynomials and
cannot be factored over the set of real numbers.
- Polynomial expressions can be used to define
functions and these functions can be represented graphically.
- There is a relationship between the factors of
any polynomial and the x-intercepts
of the graph of its related function.

· Factoring reverses polynomial multiplication.

· Trinomials may be factored by various methods including factoring by grouping.

Example of
factoring by grouping

2*x*^{2} + 5*x* – 3

2*x*^{2} + 6*x* – *x* – 3

2*x*(*x*
+ 3) – (*x* + 3)

(*x* + 3)(2*x* – 1)

· Prime polynomials cannot be factored over the set of integers into two or more factors, each of lesser degree than the original polynomial.

### ESSENTIALS

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

A.2c_{1}
**Factor** completely first-and
second-degree polynomials w/ integral coefficients

·
A.2c_{1 }**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.

A.2c_{2}
**Identify** prime polynomials

A.2c_{3}
**Use** the x-intercepts from the
graphical representation of the polynomial to **determine** and **confirm**
its factors

·
A.2c_{2 }**Factor**
and **verify** algebraic factorizations
of polynomials with a graphing utility.

### KEY VOCABULARY

monomial expression, ratio, exponents, integers,
sums, difference, product, quotient, polynomial, operations, concrete,
pictorial, factors, factor, binomial, divisor, degree, integral coefficients,
prime, x-intercepts, graphical representation

*Updated: Oct 27, 2017*