# 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 variable.

### 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

2016 VDOE Curriculum Framework - AI.2 Understanding

·  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.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.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: Jul 30, 2019