Powerpoint presentation
- 1. WELCOME
- 3. POLYNOMIALS
- 4. 1. DEGREE OF POLYNOMIALS 2. TYPES OF POLYNOMIALS ON THE BASIS OF DEGREE. 3. VALUE OF POLYNOMIALS 4. ZERO POLYNOMIAL 5. REMAINDER THEOREM 6. EXAMPLES OF SOME POLYNOMIALS
- 5. An expression containing variables, constant and any arithmetic operation is called polynomials Eg: 6x-8= 5 6→ coefficient x→ variable 8 & 5→constants NOT A POLYNOMIAL An expression like 2÷y-3, 2÷x-4 are not polynomials
- 6. Polynomials are of three types:- 1. Monomial : A Polynomial with one term 2. Binomial : A polynomial with two terms 3. Trinomial : A polynomial with three terms Eg: 4xy 6x-1 6x2+2y-2 Monomial Binomial Trinomial
- 7. Degree of polynomial – The highest power of x in P(x) is called the degree of the polynomial p(x) Example:- P(x)=3x+4 is a polynomial in the variable x of degree 1 g(y)=4y3+3x2- 4 is a polynomial in the variable y of degree 3
- 8. 1.Constant Polynomials-Polynomials having degree zero Eg: 33X0=33 , -10X0= -10 2. Quadratic Polynomial-Polynomials having degree 2. Eg: 4x2 +3x-5 3.Linear Polynomial-Polynomials having degree 1 Eg: x + 6 4. Cubic Polynomial- Polynomials having degree 3 Eg: 6x3 + 2x2 + 6x-6 5. Bi-quadratic polynomial-Polynomial having degree 4 Eg:6x4 + 3x3 - 2x2 + 3x - 8
- 9. If p(x) is a polynomial in x and if “b” is any real constant, a number obtaining replacing ‘x’ by ‘b’ in p(x) Example: p(x) = 2x2+4, then putting x =3 P(3)= 2 x (3)2 + 4=22
- 10. A real number k is said to a zero of a polynomial p(x). If said to be a zero of a polynomial p(x). If p(k)= 0 Example: p(x)= x2- 3x + 4 p(+1)= (-1)2- 3x -1+4 = 0 p(4) = (4)2 – 3x 4 – 4 = 0 Therefore -1 and 4 are called the zeros of the quadratic polynomial x2 – 3x – 4.
- 11. Let p(x) be a polynomial. Let ‘a’ be any real number. The remainder obtain p(x) is divided by x-a is p(a).
- 12. 1. 15 + 3x 2. 4x2 + 35x-15 3. 35x-24x2+ 4x3 4. X2+14x+40 5. X4+2x3=3x2+4x+3 6. 20-9 x 7. X2+x 8. 10x-x2
- 13. THANK YOU