Exit card :1 Topic :Polynomials Key words: classification of polynomials on the basis of degree, formation of quadratic polynomial,finding zeroes of cubic/ bi-quadraic polynomials when two zeroes are given. Q1 Degree of zero polynomial is ---------. Q2 A polynomial of degree 0 is called ----. Q3 write the geometrical meaning of the zeroes of the polynomials. Q4 Find a cubic polynomial whose zeroes are 2, -3 and 5. Q5 which part of the topic is tough ?
Answers
Answer:
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer. The term order has been used as a synonym of degree but, nowadays, may refer to several other concepts (see order of a polynomial (disambiguation)). For example, the polynomial {\displaystyle 7x^{2}y^{3}+4x-9,} which can also be expressed as {\displaystyle 7x^{2}y^{3}+4x^{1}y^{0}-9x^{0}y^{0},} has three terms. The first term has a degree of 5 (the sum of the powers 2 and 3), the second term has a degree of 1, and the last term has a degree of 0. Therefore, the polynomial has a degree of 5, which is the highest degree of any term.
To determine the degree of a polynomial that is not in standard form (for example:{\displaystyle (x+1)^{2}-(x-1)^{2}}), one has to put it first in standard form by expanding the products (by distributivity) and combining the like terms; for example {\displaystyle (x+1)^{2}-(x-1)^{2}=4x} is of degree 1, even though each summand has degree 2. However, this is not needed when the polynomial is expressed as a product of polynomials in standard form, because the degree of a product is the sum of the degrees of the factors