Adding & Subtracting Polynomials

Lesson 10.1

4 3 2 1 0

In addition to level 3.0 and above and

beyond what was taught in

class,  the student may:·         Make

connection with other concepts in

math·         Make

connection with other content

areas.

The student will be able to use properties of rational and irrational numbers to write, simplify, and interpret expressions on contextual situations.- justify the  sums and products of rational and irrational numbers-interpret expressions within the context of a problem

The student will be able to use properties of rational and irrational numbers to write and simplify  expressions based on contextual situations.-identify parts of an expression  as related to the context and to each part

With help from the

teacher, the student has

partial success with real number expressions.

Even with help, the

student has no success with real number

expressions.

Learning Goal 1 (HS.N-RN.B3 and HS.A-SSE.A.1):The student will be able to use properties of rational and irrational numbers to write, simplify, and interpret expressions based on contextual situations.

Polynomial:

Poly: Many nomial: terms

Form: axk

Where k is a non-negative integer.

This is a polynomial in one variable.k is the degree of ax.ax alone has a degree of 1

The constant “a” has a degree of 0.

Degree: the degree of a polynomial is the largest degree of its terms.

Standard form: terms are written in descending order from the largest to the smallest degree.Coefficient: the integer in front of the variable. How many you have of each variable. If no number, you have one.

Put this in standard form.

-4x2 + 3x3 + 2

3x3 – 4x2 + 2

Name the coefficients and degree.

2x3 + (-1)x2 + 5

-5x2 + 10x - 3

Coefficients: 2, -1

Degree: 3

Coefficients: -5, 10Degree: 2

Classifying Polynomials

Polynomial Polynomial Degree

Classify Degree of Polynomial

Classify Polynomial Terms

6 0 Constant Mononomial

-2x 1 Linear Mononomial

3x+1 1 Linear Binomial

-x2+2x-5 2 Quadratic Trinomial

4x3-8x 3 Cubic Binomial

2x4-7x3-5x+1

4 Quartic Polynomial

Adding Polynomials: add like terms!

You add the coefficients, not the variables!

(2x2+x-5) + (x2+x+6)remove ( )

= 2x2+x2+x+x-5+6

=3x2+2x+1

Horizontal format:

Vertical format: line up like terms and add.

(2x2+x-5) + (x2+x+6) remove ( ) and line up like terms.

2x2+x-5

+ x2+x+6

3x2+2x+1

Subtracting polynomials: use either vertical or horizontal format.

***Remember to change the signs of every term in the second polynomial when you remove the ( )!

Vertical format:

(8x4-3x2-11x-3) – (-13x4-3x2+2x-17)

8x4 - 3x2- 11x - 3

13x4+3x2-2x+17 (combine after changing signs)

21x4 -13x+14

Horizontal format:

(8x4-3x2-11x-3) – (-13x4-3x2+2x-17)

Remove ( ) changing the signs in the second polynomial. You are adding the opposites!8x4-3x2-11x-3 + 13x4+3x2-2x+17 (now

combine like terms)

21x4-13x+14

Classify this by degree and terms.

Quartic, trinomial

Find the area of the shaded region.

x

2x

4x2

- =

A= bh-bh

= x 2x – 4

= 2x2 – 2x2

x