SOME FORMULA FOR POLYNOMIALS

polynomials are algebraic expressions that consist of variables and coefficients. We can perform arithmetic operations such as addition, subtraction, multiplication and division in a polynomial functions. There are many types of polynomial equations. General form of polynomial equation is: $\\$ $$ a_0 x^n + a_1 x^{n-1} + a_2 x^{n-2}\cdots a_{n-1} x + a_n = 0 $$ It is a $n$ degree polynomial equation, in this equation $(a_0, a_1, a_2,\cdots a_n)$ are the coefficients. for $n$ degree polynomial $a_0 \neq 0$ $\\$ $1.$ If highest degree of $x$ is $1$ , it is called linear equation $\\$ $2.$ If highest degree of $x$ is $2$ , it is called quadratic equation $\\$ $3.$ If highest degree of $x$ is $3$ , it is called cubic equation $\\$ $4.$ If highest degree of $x$ is $4$ , it is called quartic or biquadratic equation $\\$ Let's see some basic formula for solving quadratic and cubic equations $\\$ $$ (a+b)^2 = a^2 + 2ab + b^2 \\ (a-b)^2 = a^2 -2ab+b^2 \\ (a+b)^2 = (a-b)^2 +4ab\\ (a+b)^2 + (a-b)^2 = 2(a^2 +b^2) \\ (a+b)^3 = a^3+b^3+3ab(a+b)\\ (a-b)^3 = a^3-b^3-3ab(a-b)\\ a^2-b^2 = (a+b)(a-b) \\ a^3-b^3 = (a-b)(a^2+b^2+ab) \\ a^3+b^3 = (a+b)(a^2+b^2-ab) \\ (a+b+c)^2 = a^2 +b^2 +c^2+2(ab+bc+ca) \\ (a+b-c)^2 = a^2+b^2+c^2+2(ab-bc-ca) \\ (a-b-c)^2 = a^2+b^2+c^2+2(-ab+bc-ca) \\ (a+b+c)^3 = a^3+b^3+c^3+3(a+b)(b+c)(c+a)\\ (a^3+b^3+c^3+3abc) = (a+b+c)(a^2+b^2+c^2-ab-bc-ca) $$ if $(a+b+c)=0$ , then $ a^3+b^3+c^3 = 3abc $.