Polynomials Class 9 Notes Maths - Chapter 2
What Are Polynomial ?
Meaning Of A Polynomial
- A polynomial in one variable, say x, is an algebraic expression of the form P(x) = anxn + an-1 xn-1 +.......a2x2 + a1x + a0 , where a0, a1, a2,.......,an are constants and respectively known as coefficients of x0, x, x2......., xn.
Terms Of A Polynomial
Degree Of A Polynomial
Types Of Polynomials
According to Number of Terms:
• Polynomials having only one term are called monomials.
• Polynomials having only two terms are called binomials.
• Polynomials having only three terms are called trinomials.
According to Degree:
• A polynomial of degree 0 is called constant polynomial.
• A polynomial of degree 1 is called linear polynomial.
• A polynomial of degree 2 is called quadratic polynomial.
• A polynomial of degree 3 is called cubic polynomial.
• A polynomial of degree 4 is called biquadratic polynomial.
Zeroes Of A Polynomial
• Any real number `k’ is called a zero of a polynomial p(x), if p(K) = 0
• If `k’ is the zero of p(x), then we can also say `k’ is a root of the equation p(x) = 0
Some Important Facts
• Every linear polynomial in one variable has a unique zero.
• Every non-zero constant polynomial has no zero.
• Every real number is a zero of the zero polynomial
If p(x) is any polynomial of degree n (n ≥ 1) and p(x) is divided by the linear polynomial x – a, then the remainder is p(a).
x – a is a factor of the polynomial p(x), if p(a) = 0 and vice versa, i.e. if x – a is a factor of p(x), then p(a) = 0
• (x + a) (x + b) = x2 + (a + b) x + ab