#### Math - 2017-18

# A.2ab and *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;

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

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

**Bloom's Level:** Apply

*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.

· 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.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**
sum and difference of polynomials w/concrete objects and their related
pictorial representations.

A.2b_{1} **Model**
products of polynomials w/ concrete objects
and their related pictorial representations.

A.2b_{1} **Model**
quotients of polynomials w/ concrete objects and related pictorial
representations.

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

A.2b_{2} **Relate**
concrete and pictorial manipulations that model polynomial operations to their
corresponding symbolic representations.

A.2b_{3} **Find**
sums and differences of polynomials.

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

A.2b_{4} **Find**
the products of polynomials. The factors will have no more than five total
terms.

·
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_{5} **Find**
the quotient of polynomials, using a monomial or binomial divisor, or a
complete factored divisor.

·
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: Oct 27, 2017*