# 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.2  The student will perform operations on polynomials, including

c)  factoring completely first- and second-degree binomials and trinomials in one variable.

Bloom's Level:  Analyze

### 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
2x2 + 5x – 3
2x2 + 6xx – 3
2x(x + 3) – (x + 3)
(x + 3)(2x – 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.2c1  Factor completely first-and second-degree polynomials w/ integral coefficients

·  A.2cFactor 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.2c2  Identify prime polynomials

A.2c3  Use the x-intercepts from the graphical representation of the polynomial to determine and confirm its factors

·  A.2cFactor 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