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Adding & Subtracting Polynomials: solving and understanding

Learn how to solve and understand adding and subtracting polynomials with step-by-step examples. Improve your algebraic skills!

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Adding & Subtracting Polynomials: solving and understanding

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

  2. Adding & Subtracting Polynomials 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.

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

  4. Real Life Application You are enlarging a 5-inch by 7-inch photo by a scale factor of xand 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. Write a model for the area of the mat around the photograph as a function of the scale factor. Use a verbal model. SOLUTION Area of photo Area of mat = Total Area – Verbal Model 7x 14x – 2 Area of mat = A (square inches) Labels 5x Total Area = (10x)(14x – 2) (square inches) 10x Area of photo = (5x)(7x) (square inches) …

  5. Real Life Application A model for the area of the mat around the photograph as a function of the scale factor x is A = 105x2 – 20x. SOLUTION (10x)(14x – 2) –(5x)(7x) A = 7x 14x – 2 … = 140x2 – 20x – 35x2 5x Algebraic Model = 105x2 – 20x 10x

  6. 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: Vocabulary

  7. 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

  8. Adding Polynomials Horizontal (5x2 + 4x + 1) + (2x2 + 5x + 2)= Vertical: 5x2 + 4x + 1 + 2x2 + 5x + 2 Adding Polynomials

  9. Subtracting Polynomials All signs for each term must be flipped in the set of parentheses that follow the subtraction sign. (16y2 – 8y + 9) – (6y2 – 2y + 7y) (16y2 – 8y + 9) + (- 6y2+ 2y - 7y) Change the signs, then add. Subtracting Polynomials

  10. Subtracting Polynomials Horizontal (5x2 + 14x + 6) - (2x2 - 5x - 2) = Vertical: 5x2 + 10x + 9 - 2x2 + 5x + 2 Subtracting Polynomials

  11. Example 1 Add (4x2 + 6x + 7) + (2x2— 9x + 1)

  12. Example 2 Subtract (3x2 – 2x + 8) – (x2 – 4) Adding Polynomials

  13. You try Add or Subtract • (x2 + x + 1) + (x2 – 2x + 4) • (-2x3 + 5x2 – x +8) - (-2x3+3x – 4) • (x2 – 8) - (7x + 4x2) • (3x2 – 5x +3) + (2x2- x – 4) Subtracting Polynomials

  14. Exit Slip Add or Subtract • (4x2 + 3x) - (6x2 – 5x + 2) • (-10m3 – 3m + 4m2) – (3m3+ 5m) • (2w2 – 4w - 12) + (15 – 3w2 + 2w) • (-10x2 + 3x – 4x3) – (3x3 – 5x -16x2) Subtracting Polynomials

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