Do Now:

JournalExplain each of the following rules of exponents:

1. Product of Powers

2. Quotient of Powers

3. Power of Powers

4. Zero Exponent

January 25, 2013

Adding and Subtracting PolynomialsEssential Question:

How can I use Polynomials to represent real life situations?

Vocabulary

Polynomial – sum of terms in the form of axk where k is a nonnegtive integer.

Example – 2x3 + 5x2 -4x + 7

Standard Form – Terms are placed in descending order from largest degree to smallest degree

Degree – the degree of each term of a polynomial is the exponent of the variable.

Leading Coefficient – When written in its standard form, the coefficient of the first term.

Identify Polynomial Coefficients

-4x2 + x3 + 3

Write the Polynomial in standard form. (Account for each degree)

THIS SHOULD BE WRITTEN:X3 - 4x2 + 3

POLYNOMIALS

MONOMIAL – POLYNOMIAL WITH ONE TERM ( -2X)

BINOMIAL – POLYNOMIAL WITH TWO TERMS(3X + 1)

TRINOMIAL – POLYNOMIAL WITH THREE TERMS(X2 + 2X + 6)

Classifying Polynomials by Degree

POLYNOMIAL DEGREE CLASSIFIED BY DEGREE

CLASSIFIED BY TERMS

6 0 CONSTANT MONOMIAL

2X 1 LINEAR MONOMIAL

3X + 1 1 LINEAR BINOMIAL

X2 + 2X + 5 2 QUADRATIC TRIOMIAL

4X3 + 8X 3 CUBIC BINOMIAL

2X3 + X2 – 5x + 1 3 CUBIC POLYNOMIAL

ADDING POLYNOMIALS: LETS REMEMBER LIKE TERMS

WE CAN ONLY ADD TERMS WITH LIKE VARIABLES AND

LIKE COEFICIENTS

Adding PolynomialsFind the sum. Write the answer in standard form.

(5x3 – x + 2 x2 + 7) + (3x2 + 7 – 4x) + (4x2 – 8 – x3)

Vertical Format: Write each expression in standard form. Align like terms.

5x3 + 2x2 – x + 7 3x2 – 4x + 7 -x3 + 4x2 - 8 4x3 + 9x2 – 5x + 6

Subtracting Polynomials

Find the difference.

(x2 – 8) – (7x + 4x2)

Vertical Format: To subtract, distribute the negative to all terms inside the parenthesis. (X2 – 8) -(7x + 4x2)

Using Polynomials in Real Life

You are enlarging a 5 inch by 7 inch photo by a scale factor of x and mounting it on a mat. You want the mat to be twice as wide as the enlarged photo and 2 inches less than twice as high as the enlarged photo.a. Draw a digram to represent the described

situation.b. Write a model for the area of the mat

around the photograph as a function of the scale factor.

Using Polynomials in Real Life

The dimensions of the photo are enlarged by a scale factor of x

5x

7x

10x

14x -2