In your notebook: Explain why 5xy 2 + 3x 2 y is NOT equal to 8x 3 y 3 ? Then correctly solve it.

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Presentation transcript:

In your notebook: Explain why 5xy 2 + 3x 2 y is NOT equal to 8x 3 y 3 ? Then correctly solve it.

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

Standard 10.0 Students add, subtract, multiply and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.

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) Total Area – Use a verbal model. 5x5x 7x7x 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. Algebraic Model … 5x5x 7x7x 14x – 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:

* Adding Polynomials 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 Polynomials Horizontal (5x 2 + 4x + 1) + (2x 2 + 5x + 2) = Vertical: 5x 2 + 4x x 2 + 5x + 2

* Subtracting Polynomials All signs for each term must be flipped in the set of parentheses that follow the subtraction sign. (16y 2 – 8y + 9) – (6y 2 – 2y + 7y) (16y 2 – 8y + 9) + (- 6y 2 + 2y - 7y) Change the signs, then add.

* Subtracting Polynomials Horizontal (5x x + 6) - (2x 2 - 5x - 2) = Vertical: 5x x x 2 + 5x + 2

Add (4x 2 + 6x + 7) + (2x 2— 9x + 1)

* Adding Polynomials Subtract (3x 2 – 2x + 8) – (x 2 – 4)

* Subtracting Polynomials Add or Subtract 1. (x 2 + x + 1) + (x 2 – 2x + 4) 2. (-2x 3 + 5x 2 – x +8) - (-2x 3 +3x – 4) 3. (x 2 – 8) - (7x + 4x 2 ) 4. (3x 2 – 5x +3) + (2x 2 - x – 4)

* Subtracting Polynomials Add or Subtract 1. (4x 2 + 3x) - (6x 2 – 5x + 2) 2. (-10m 3 – 3m + 4m 2 ) – (3m 3 + 5m) 3. (2w 2 – 4w - 12) + (15 – 3w 2 + 2w) 4. (-10x 2 + 3x – 4x 3 ) – (3x 3 – 5x -16x 2 )