Adding and Subtracting Polynomials

Adding and Subtracting Polynomials A polynomial is an expression of power n where n= 0, 1, 2, 3 n Where n is a positive integer. Degree of a polynomial in one variable: - In case of a polynomial in one variable, the highest power of the variable is called the degree of polynomial. Polynomial of various degrees Linear polynomial: - a polynomial of degree 1 is called a linear polynomial. Quadratic polynomial: - A polynomial of degree 2 is called a quadratic polynomial. Cubic polynomial: - A polynomial of degree 3 is called a cubic polynomial. Biquadratic polynomial: - A polynomial of degree 4 is called a biquadratic polynomial. Number of terms in a polynomial: - Monomial: - A polynomial containing one nonzero term is called a monomial. Binomial: - A polynomial containing two nonzero terms is called a binomial. Trinomial: - A polynomial containing three nonzero terms is called a trinomial. Example of adding and subtracting polynomials: - Question1: - Add the following polynomials y^4 + 2y^2 + 3y + 5 and 5y^4 + 4y^3 + 3y^2 + 5y Solution: - (y^4 + 2y^2 + 3y + 5) + (5y^4 + 4y^3 + 3y^2 + 5y) =(y^4 + 5y^4) + 4y^3 + (2y^2 + 3y^2) + (3y + 5y) + 5 =6y^4 + 4y^3 + 5y^2 + 8y + 5 Question2: - Subtract the following polynomials: Z^3 + 2z + 1 and z^2 + 3z + 5 Solution: - (z^3 + 2z + 1) - (z^2 + 3z + 5) =z^3 + 2z + 1 z^2 -3z -5 =z^3 z^2 z -4