. Introduction In Class IX, you have studied polynomials in one variable and their degrees. Recall that if p ( x ) is a polynomial in x , the highest power of x in p ( x ) is called the degree of the polynomial p ( x ). For example, x + is a polynomial in the variable x of degree , y – y + is a polynomial in the variable y of degree , x – x + x – is a polynomial in the variable x of degree and u – u u u is a polynomial in the variable u of degree .
Expressions like x x etc., are not polynomials. A polynomial of degree is called a linear polynomial . For example, x – , , x y x , z + , u , etc., are all linear polynomials. Polynomials such as x + – x , x + , etc., are not linear polynomials.
A polynomial of degree is called a quadratic polynomial . The name ‘quadratic’ has been derived from the word ‘quadrate’, which means ‘square’. , y – , , , , u u v v z are some examples of quadratic polynomials (whose coefficients are real numbers). More generally, any quadratic polynomial in x is of the form ax + bx + c , where a , b , c are real numbers and a .
A polynomial of degree is called a cubic polynomial . Some examples of a cubic polynomial are – x , x , – x + x , x – x + x – . In fact, the most general form of a cubic polynomial is ax + bx + cx + d , where, a , b , c , d are