A Polynomial is an algebraic expression that contains finite number of terms with non-zero coefficients. In other words, it can be described as an expression that contains finite number of terms with combination of variables, whole number exponents of variables and consonants.
Types of Polynomials:
- Monomial- A polynomial having only one term is known as a Monomial. Eg., 2x2, 7xy.
- Binomial- "Bi" means two. Therefore, a polynomial having two terms is known as a Binomial. Eg., 2x+5, 5x2 6.
- Trinomial- The word “tri” means three. Hence, a polynomial with three terms is known as a Trinomial. Eg., 2x2-4x+5,
Degree of Polynomial
The exponent in the term having the highest power is known as the “degree of polynomial”. Example, in the equation 7x5+4x4-6x3-5x2+6, the term with the highest power is 7x5. Therefore, the degree of polynomial in this equation will be 5.
- A linear polynomial is a polynomial of degree 1.
It is of the form ax+b where a≠0.
- A quadratic polynomial is a polynomial of degree 2.
It is of the form ax2+bx+c where a≠0.
Division of a Polynomial by a Polynomial
Let p(x) and f(x) be the two polynomials where f(x) ≠0. Then, we can find polynomials q(x) and r(x), such that p(x) - f(x) . q(x) + r(x), where degree r(x) < degree f(x). Therefore, we can say that p(x) when divided by f(x) gives q(x) as a quotient and r(x) as the remainder.
If the remainder r(x) is zero, then we can say that divisor f(x) is a factor of p(x) and we have, p(x) = f(x) . q(x).
Like Terms and Unlike Terms
- Like terms contains the same variables having same powers.
- Unlike terms contains different variables having different powers.