Chapter 2 What is polynomial ? "An expression that contains different power of same variable in algrebaic form " . Example : P(x) = 2x + 5 , P(y) = y 2 + 5y + 6 What is the Degree Of polynomial ? " Degree of polynomial is the highest power of variable in given polynomial. " For Example : P(x) = 2x + 5 has one as the highest power of x , so degree of polynomial is 1 similarly P(y) = y 2 + 5y + 6 is 2 as the highest power of y , degree polynomial. Linear Polynomial : Polynomial having degree '1' Quadratic Polynomial : Polynomial having degree '2' Cubic Polynomial : Polynomial having degree '3' Zeroes of a polynomial : A real number K is said to be zero of polynomial , If P(K) = 0 Example : P(x) = x + 5 For x = -5 ⇒ P(-5) = 0 So , -5 is the zero of the polynomial. Geometrical meaning Of zeroes : If we plot or draw any polynomial on x-y plane, and the curve cuts the x-axis at ...

Chapter 1 Euclid Division Algorithm: Given positive integers a and b , there exist unique integers q and r satisfying a = bq + r , 0 ≤ r < b How to find HCF and LCM using Euclid's Algorithm I) 135 and 225 let a = 225 , b = 135 Apply Euclid's Algorithm till remainder becomes zero , the corresponding divisor will be the HCF 225 = 135 × 1 + 90 135 = 90 × 1 + 45 90 = 45×2 + 0 So , HCF = 45 . I) 455 and 42 let a = 455 , b = 42 Apply Euclid's Algorithm till remainder becomes zero , the corresponding divisor will be the HCF 445 = 42 ×10 + 35 42 = 35 × 1 + 7 35 = 7×5 + 0 So , HCF = 7 . Fundamental theorem of Arithmetic: "Every Composite number can be expressed as a product of primes and this factorizaion is unique." Example : Let's take a composite number '12' It can be written as factorization of prime numbers. i.e. 12 = 2 ×2 ×3 and this factorization is unique. this is the fundamental the...