Quick Review: Polynomials

Polynomials
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.
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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).
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Like Terms and Unlike Terms
  • Like terms contains the same variables having same powers.
  • Unlike terms contains different variables having different powers.