5 3 Adding Polynomials Adding Polynomials with Algebra

5. 3 Adding Polynomials

Adding Polynomials with Algebra Tiles • We can use algebra tiles to model an addition sentence. (3 s 2 + 2 s – 6) + (-s 2 – 2 s + 1) Combine the tiles and group the matching tiles.

• Remove the zero pairs. • The remaining tiles are: • They represent 2 s 2 - 5

Adding polynomials Symbolically • Add: (3 c 2 + 5 c – 6) + (2 c 2 – 3 c + 4) • Remove the brackets. = 3 c 2 + 5 c – 6 + 2 c 2 – 3 c + 4 • Group like terms. = 3 c 2 + 2 c 2 + 5 c – 3 c – 6 +4 • Add the coefficients of like terms. = 5 c 2 + 2 c - 2

Determining a polynomial for the perimeter of a rectangle • Write a polynomial for the perimeter of the rectangle. 2 x + 1 3 x + 2 • The perimeter is the sum of all 4 sides. (2 x + 1) + (3 x + 2) = 10 x + 6

Adding polynomials in 2 variables (2 a 2 + a – 3 b – 7 ab + 3 b 2) + (-4 b 2 + 3 ab + 6 b – 5 a + 5 a 2) = 2 a 2 + a – 3 b – 7 ab + 3 b 2 - 4 b 2 + 3 ab + 6 b – 5 a + 5 a 2 = 2 a 2 + 5 a 2 + a – 5 a – 3 b + 6 b – 7 ab + 3 b 2 - 4 b 2 = 7 a 2 - 4 a + 3 b – 4 ab – b 2

Adding Polynomials Vertically (2 m + 9) + (3 m 2 + m – 14) 2 m + 9 3 m 2 + 1 m – 14 3 m 2 + 3 m – 5 • Remove the brackets. • Align the like terms vertically. • The term “m” has no visible coefficient so make it 1. • Add the coefficients of the like terms.

Assignment: • Pg. 228 -230 3, 4, 8 odd, 9 odd, 10 all, 17 all