advertisement

Adding & Subtracting Polynomials A-APR.4 Objective: 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. MODELING ADDITION OF POLYNOMIALS Algebra tiles can be used to model polynomials. + – 1 –1 These 1-by-1 square tiles have an area of 1 square unit. + – + – x –x x2 –x 2 These 1-by-x rectangular tiles have an area of x square units. These x-by-x rectangular tiles have an area of x 2 square units. MODELING ADDITION OF POLYNOMIALS You can use algebra tiles to add the polynomials x 2 + 4x + 2 and 2 x 2 – 3x – 1. 1 Form the polynomials x 2 + 4x + 2 and 2 x 2 – 3x – 1 with algebra tiles. x2 + 4x + 2 + + + + + + + – 2 x2 + + – 1 3x – – – – MODELING ADDITION OF POLYNOMIALS You can use algebra tiles to add the polynomials x 2 + 4x + 2 and 2 x 2 – 3x – 1. 2 To add the polynomials, combine like terms. Group the x 2-tiles, the x-tiles, and the 1-tiles. x 2 + 4x + 2 + + + + + + + + 2x 2 – 3x – 1 + + – + + + + + + + + + = + – – – – – – – MODELING ADDITION OF POLYNOMIALS You can use algebra tiles to add the polynomials x 2 + 4x + 2 and 2 x 2 – 3x – 1. 2 3 To add the polynomials, combine like terms. Group the x 2-tiles, the x-tiles, and the 1-tiles. 2 + 4x + 2 xFind and remove the zero pairs. + + + sum is + 3x+2 + x+ + 1. + The + 2x 2 – 3x – 1 + + – + + + + + + + + + = + – – – – – – – Adding Polynomials Find the sum. Write the answer in standard format. (2 x 2 + x – 5) + (x + x 2 + 6) SOLUTION Horizontal format: Add like terms. (2 x 2 + x – 5) + (x + x 2 + 6) = (2 x 2 + x 2) + (x + x) + (–5 + 6) = 3x 2 + 2 x + 1 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. Write a model for the area of the mat around the photograph as a function of the scale factor. Use a verbal model. Verbal Model Area of mat = Total Area – Labels … Area of photo 7x Area of mat = A (square inches) 5x Total Area = (10x)(14x – 2) (square inches) 10x Area of photo = (5x)(7x) (square inches) 14x – 2 SOLUTION 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. Write a model for the area of the mat around the photograph as a function of the scale factor. SOLUTION … = 140x 2 – 20x – 35x 2 5x = 105x 2 – 20x 10x 14x – 2 Algebraic Model 7x A = (10x)(14x – 2) – (5x)(7x) A model for the area of the mat around the photograph as a function of the scale factor x is A = 105x 2 – 20x.