#### Math - 2019-20

# A.2ab - Polynomials

A.2The student willperformoperations on polynomials, includinga) applying the laws of exponents to perform operations on expressions;

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

*Adopted: 2016*

### 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

· 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

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.

· 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.2a_{1 }**Simplify**
monomial expressions and ratios of monomial expressions in which the exponents
are integers, using the laws of exponents.

·
A.2b_{1 }**Model**
sums, differences, products, and quotients of polynomials with concrete objects
and their related pictorial and symbolic representations.

·
A.2b_{2 }**Determine**
sums and differences of polynomials.

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

·
A.2b_{4 }**Determine**
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: Jul 30, 2019*