4.2 Adding and Subtracting Polynomials Objective: To add and subtract polynomials. Warm – up: Simplify: 1) 6x + 7y + 4x2) m – 6 + 4m 3) -(5a – 2b + 7)4) 4z + 3 – 2 + 7z

4.2 Adding and Subtracting Polynomials Definitions o Monomial – an expression that is either a numeral, a variable or the product of these. o Polynomial – a sum of monomials o Polynomials with special names: o Binomials – a sum of two terms o Trinomials – a sum of three terms o Coefficient – the numeral within the monomial o Similar Terms – monomials with like variables. These terms can be combined! Examples o 14, z,, -6x 2 y o x 2 + (-4x) + (-5) = x 2 – 4x – 5 o 2x – 9, 2ab + b 2 o x 2 – 4x – 5, a 2 + 3ab – 4b 2 o -3 xy o -5xy 2, 16yxy, xy 2, -3x 2 y, 5xy

4.2 Adding and Subtracting Polynomials Name the similar polynomials: o -2x, 2xy, 4y, x, -xy, -y o -st 2, 2s 2 t, 3t 2 s, -s 2 t o 3a 4, -4a 3, a 2, 5a 3, 3a 2 o x 2 y 2, x 2, y 2, -3x 2 y 2, -4x 2 Simplify: o -6x 3 + 3x 2 + x 2 + 6x 3 – 5 o -3x 2 + 5x – 2x + x 2 – 4 o -4m 2 + 5mn 2 – m 2 + 3mn 2

4.2 Adding and Subtracting Polynomials Find the degree. o The degree of a polynomial is the greatest of the degrees of its terms after it has been simplified. o 5x 2 yz 4 o 4x 3 yz 2 Add the Polynomials o (2x – 5) + (x + 3) o (2a – b + 1) + (-a – b + 3)

4.2 Adding and Subtracting Polynomials Add the Polynomials: o (2a 2 + ab + 2b) + (4a 2 – 3ab + 9) o (3x 2 y + 4xy 2 – 2y 3 + 3) + (x 2 y + 3y 3 – 4) o o

4.2 Adding and Subtracting Polynomials Sum of Rectangles! o Write the sum of the rectangles as a polynomial in simplest form. 3x 2 x x 3 3 3x 2 Homework: – Pg. 148 Written Exercises #1 – 20 – Challenge Problems: #31, 32, 37, 38, 41, 42