What is trinomial naminlatune?
Answers
A polynomial with three terms is called a trinomial. Trinomials often (but not always!) have the form x2 + bx + c. At first glance, it may seem difficult to factor trinomials, but you can take advantage of some interesting mathematical patterns to factor even the most difficult-looking trinomials.
Explanation:
Trinomial expressions Edit
{\displaystyle 3x+5y+8z}3x+5y+8z with {\displaystyle x,y,z}x, y, z variables
{\displaystyle 3t+9s^{2}+3y^{3}}3t+9s^{2}+3y^{3} with {\displaystyle t,s,y}t,s,y variables
{\displaystyle 3ts+9t+5s}3ts+9t+5s with {\displaystyle t,s}t,s variables
{\displaystyle Ax^{a}y^{b}z^{c}+Bt+Cs}Ax^{a}y^{b}z^{c}+Bt+Cs with {\displaystyle x,y,z,t,s}x,y,z,t,s variables, {\displaystyle a,b,c}a,b,c nonnegative integers and {\displaystyle A,B,C}A,B,C any constants.
{\displaystyle Px^{a}+Qx^{b}+Rx^{c}}Px^{a}+Qx^{b}+Rx^{c} where {\displaystyle x}x is variable and constants {\displaystyle a,b,c}a,b,c are nonnegative integers and {\displaystyle P,Q,R}P,Q,R any constants.
Trinomial equation Edit
A trinomial equation is a polynomial equation involving three terms. An example is the equation {\displaystyle x=q+x^{m}}x=q+x^{m} studied by Johann Heinrich Lambert in the 18th century.[2]
Some notable trinomials Edit
sum or difference of two cubes:
{\displaystyle (a^{3}\pm b^{3})=(a\pm b)(a^{2}\mp ab+b^{2})}{\displaystyle (a^{3}\pm b^{3})=(a\pm b)(a^{2}\mp ab+b^{2})}
A special type of trinomial can be factored in a manner similar to quadratics since it can be viewed as a quadratic in a new variable (xn below). This form is factored as:
{\displaystyle x^{2n}+sx^{n}+p=(x^{n}+a_{1})(x^{n}+a_{2}),}{\displaystyle x^{2n}+sx^{n}+p=(x^{n}+a_{1})(x^{n}+a_{2}),}
where
{\displaystyle {\begin{aligned}a_{1}+a_{2}&=s\\a_{1}\cdot a_{2}&=p.\end{aligned}}}{\displaystyle {\begin{aligned}a_{1}+a_{2}&=s\\a_{1}\cdot a_{2}&=p.\end{aligned}}}
For example, the polynomial (x2 + 3x + 2) is an example of this type of trinomial with n = 1. The solution a1 = 2 and a2 = 1 of the above system gives the trinomial factoring:
(x2 + 3x+ 2) = (x + a1)(x + a2) = (x + 2)(x + 1).
The same result can be provided by the Ruffini's rule, but with a more complex and time-consuming process.