In your notebook:Explain why 5xy2 + 3x2y is NOT equal to 8x3y3? Then correctly solve it.

Objective: Objective: Students will be able to Students will be able to demonstrate their understanding demonstrate their understanding of adding and subtracting of adding and subtracting polynomials by 1) correctly polynomials by 1) correctly solving at least 2 of the 4 “you solving at least 2 of the 4 “you try” problems, 2) completing the try” problems, 2) completing the polynomial puzzle, and 3) polynomial puzzle, and 3) correctly solving at least 3 out of correctly solving at least 3 out of the 4 exit slip problems.the 4 exit slip problems.

Total Area = (10x)(14x – 2) (square inches)

Area of photo =

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.

Real Life Application

Write a model for the area of the mat around the photograph as a function of the scale factor.

Verbal Model

Labels

Area of mat =

Area of photo

Area of mat = A

(5x)(7x)

(square inches)

(square inches)

Total Area –

Use a verbal model.

5x

7x

14x – 2

10x

SOLUTION

…

(10x)(14x – 2) – (5x)(7x)

Real Life Application

A =

= 140x 2 – 20x – 35x

2

SOLUTION

= 105x 2 – 20x

A model for the area of the mat around the photograph as a function of the scale factor x is A = 105x 2 – 20x.

AlgebraicModel

…

5x

7x14x – 2

10x

1. A monomial is an expression that is a number, a

variable, or a product of a number and one or

more variables. Ex:

2. A polynomial has two or more terms. Ex:

3. Standard form is the form of a polynomial in

which the degree of the terms decreases from left

to right.

Ex:

65212 xx

932315 xxx

27x

*Adding Adding PolynomialsPolynomials

Adding polynomials involves adding like terms.

We can group like terms horizontally or vertically.

Answers should be in standard form.

If there is more than one variable, put in alpha order.

*Adding Adding PolynomialsPolynomials

Horizontal (5x2 + 4x + 1) + (2x2 + 5x + 2) =

Vertical: 5x2 + 4x + 1+ 2x2 + 5x + 2

*Subtracting Subtracting PolynomialsPolynomials

All signs for each term must be flipped in theset of parentheses that follow the subtractionsign.

(16y2 – 8y + 9) – (6y2 – 2y + 7y)(16y2 – 8y + 9) + (- 6y2 + 2y - 7y)

Change the signs, then add.

*Subtracting Subtracting PolynomialsPolynomials

Horizontal (5x2 + 14x + 6) - (2x2 - 5x - 2) =

Vertical: 5x2 + 10x + 9- 2x2 + 5x + 2

Add

(4x2 + 6x + 7) + (2x2— 9x + 1)

*Adding Adding PolynomialsPolynomials

Subtract

(3x2 – 2x + 8) – (x2 – 4)

*Subtracting Subtracting PolynomialsPolynomials

Add or Subtract1. (x2 + x + 1) + (x2 – 2x + 4)

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

3. (x2 – 8) - (7x + 4x2)

4. (3x2 – 5x +3) + (2x2- x – 4)

1.

*Subtracting Subtracting PolynomialsPolynomials

Add or Subtract1. (4x2 + 3x) - (6x2 – 5x + 2)

2. (-10m3 – 3m + 4m2) – (3m3+ 5m)

3. (2w2 – 4w - 12) + (15 – 3w2 + 2w)

4. (-10x2 + 3x – 4x3) – (3x3 – 5x -16x2)

1.