# A.2ab - Polynomials

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

a)  applying the laws of exponents to perform operations on expressions;

b)  adding, subtracting, multiplying, and dividing polynomials;

### 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

·  Operations with polynomials can be represented concretely, pictorially, and symbolically.

·  Polynomial expressions can be used to model practical situations.

·  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.

·  Polynomial expressions can be used to define functions and these functions can be represented graphically.

·  The laws of exponents can be applied to perform operations involving numbers written in scientific notation.

·  For division of polynomials in this standard, instruction on the use of long or synthetic division is not required, but students may benefit from experiences with these methods, which become more useful and prevalent in the study of advanced levels of algebra.

### ESSENTIALS

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

·  A.2aSimplify monomial expressions and ratios of monomial expressions in which the exponents are integers, using the laws of exponents.

·  A.2bModel sums, differences, products, and quotients of polynomials with concrete objects and their related pictorial and symbolic representations.

·  A.2bDetermine sums and differences of polynomials.

·  A.2bDetermine products of polynomials.  The factors should be limited to five or fewer terms (i.e.,  (4x + 2)(3x + 5) represents four terms and (x + 1)(2x+ x + 3) represents five terms).

·  A.2bDetermine the quotient of polynomials, using a monomial or binomial divisor, or a completely factored divisor.

### 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: Aug 23, 2018