Add and Subtract Polynomials

Add and Subtract Polynomials Definition: - An algebraic expression in which the variables involved have only non-negative integral powers is called a polynomial. Examples: - 5x^3 4x^2 + 6x -3 is a polynomial in one variable x. 9y^4 +6 y^3 + 10y^2 -8y +2/5 is a polynomial in one variable y. 3 +2x^2 -6x^2y +5xy^2 is a polynomial in two variable x and y. 5+ 8x^ (3/2) +4x^2 is an expression but not a polynomial, since it contains a term containing x^ (3/2), where 3/2 is not a non-negative integer. Note: - A polynomial containing one term only, consisting of a constant is called a constant polynomial. Example: - 3, -5, 7/8 etc. are all constant polynomial. In general, every real number is a constant polynomial. A polynomial consisting of one term, namely zero only is called a zero polynomial. Example1: - Add and subtract the following polynomials 2x^2 + 5x + 9 and 6x^2 + 8x + 3 Solution: - (2x^2 + 5x + 9) + (6x^2 + 8x + 3) = (2x^2 + 6x^2) + (5x+8x) + (9+3) = 8x^2 + 13x + 12 (2x^2 + 5x + 9) (6x^2 + 8x + 3) = 2x^2 + 5x + 9 - 6x^2 - 8x 3 = (2x^2 6x^2) + (5x 8x) + (9 3) = -4x^2 3x + 6 Example2: - Add and subtract the polynomials 2x + y 3 and 3x + 2y 8 Solution: - (2x + y 3) + (3x + 2y 8) = 2x+y 3+3x+2y8 = 5x+3y-11 (2x + y 3) - (3x + 2y 8) = 2x+y3-3x-2y+8 = -x-y+5