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A-APR.4 Objective:

A-APR.4 Objective:. Adding & Subtracting Polynomials. Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x 2 + y 2 ) 2 = (x 2 – y 2 ) 2 + (2xy) 2 can be used to generate Pythagorean triples. MODELING ADDITION OF POLYNOMIALS.

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A-APR.4 Objective:

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  1. A-APR.4 Objective: Adding & Subtracting Polynomials • Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2 can be used to generate Pythagorean triples.

  2. MODELING ADDITION OF POLYNOMIALS + – + – + – 1 –1 x –x x2 –x2 Algebra tiles can be used to model polynomials. These 1-by-1 square tiles have an area of 1 square unit. These 1-by-x rectangular tiles have an area of x square units. These x-by-x rectangular tiles have an area of x2 square units.

  3. MODELING ADDITION OF POLYNOMIALS 1 You can use algebra tiles to add the polynomials x2 + 4x + 2 and 2x2 – 3x – 1. Form the polynomials x2 + 4x + 2 and 2x2 – 3x – 1 with algebra tiles. x2 + 4x + 2 + + + + + + + 2x2 – 3x – 1 + + – – – –

  4. MODELING ADDITION OF POLYNOMIALS 2 + + + – – – + + + + + + + – + You can use algebra tiles to add the polynomials x2 + 4x + 2 and 2x2 – 3x – 1. To add the polynomials, combine like terms. Group the x2-tiles, the x-tiles, and the 1-tiles. 2x2 – 3x – 1 x2 + 4x+ 2 + + + + + + + + – = + – – –

  5. MODELING ADDITION OF POLYNOMIALS 3 2 + + + – – – + + + + + + + – + You can use algebra tiles to add the polynomials x2 + 4x + 2 and 2x2 – 3x – 1. To add the polynomials, combine like terms. Group the x2-tiles, the x-tiles, and the 1-tiles. 2x2 – 3x – 1 x2 + 4x+ 2 Find and remove the zero pairs. The sum is 3x2 + x + 1. + + + + + + + + – = + – – –

  6. Adding Polynomials Find the sum. Write the answer in standard format. (2x2 + x – 5) + (x + x2 + 6) SOLUTION Horizontal format: Add like terms. (2x2 + x – 5) + (x + x2 + 6) = (2x2 +x2) + (x + x) + (–5 + 6) = 3x2 + 2x+ 1

  7. Using Polynomials in Real Life 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) …

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

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