Class 10 Maths: Polynomials Olympiad Questions

The polynomials are the complete set of rational numbers exponents. They are algebraic expressions. Whereas in the polynomial, the variable exponent is the whole number.

Example of a polynomial:

• 2x + 2x + 3.
• 4x+3√x is not a polynomial because the 1/2 exponent of x is not a set of whole numbers.

Polynomial types:

Generally, there are three types of polynomials. These are given below:

• Monomial:

  Monomials are the terms that only consist of one term, i.e., 3x, 5x, etc.

• Binomial:

  Binomials are the terms that consist of two terms, i.e., 4x + 3, 5x + 5.

• Trinomial:

  Trinomials consist of more than two terms, i.e., x2+3x+4.

Degree of a polynomial:

The polynomial degree is the highest power that is present in the equation.

Zero of a polynomial:

• When the value of the equation results in a zero, it is known as the zero of a polynomial.
• Like p(x) at x = 0, then p(x) = 0 and that is known as the zero of the polynomial.

Polynomial zero algorithms:

• In the division algorithm of polynomials, two polynomials are given.
• Like p(y) and g(y) are the two polynomials in which g(y) is not equal to zero.
• Then it can be found with p(y) = g(y). q(y). r(y), in which r(y) = 0.