Adding and Subtracting Polynomials

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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




 

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