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, 4x + 2 is a polynomial in the variable x of degree 1, 2y 2 – 3y + 4 is a polynomial in the variable y of degree 2, 5x 3 – 4x 2 + x – 2 is a polynomial in the variable x of degree 3 and 7u 6 – 3 4 2 4 8 2 u u u + + − is a polynomial in the variable u of degree 6. Expressions like 1 x − 1 , x + 2 , 2 1 x x + + 2 3 etc., are not polynomials. A polynomial of degree 1 is called a linear polynomial. For example, 2x – 3, 3 5, x + y + 2 , 2 11 x − , 3z + 4, 2 1 3 u + , etc., are all linear polynomials. Polynomials such as 2x + 5 – x 2 , x 3 + 1, etc., are not linear polynomials. A polynomial of degree 2 is called a quadratic polynomial. The name ‘quadratic’ has been derived from the word ‘quadrate’, which means ‘square’. 2 2 2 3 , 5 x x + − y 2 – 2, 2 2 3 , − + x x 2 2 2 1 2 2 5, 5 , 4 3 3 7 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 ax2 + bx + c, where a, b, c are real numbers and a ≠ 0. A polynomial of degree 3 is called a cubic polynomial