phyguy321 said:but how do i know that (x-c1)(x-c2)...(x-cn) = xLaTeX Code: ^{n} + (c1+c2+...+cn)xLaTeX Code: ^{n-1} ...(c1*c2*...*cn)?
An nth degree polynomial is a mathematical expression that contains a variable raised to the power of n, where n is a non-negative integer. The highest power of the variable in the polynomial is known as the degree of the polynomial.
The sum of an nth degree polynomial is the result of adding all the terms of the polynomial. This is achieved by combining like terms, which means simplifying terms that have the same variable and exponent. The sum of an nth degree polynomial can also be represented as a polynomial of the same degree.
The product of an nth degree polynomial is the result of multiplying all the terms of the polynomial. This is achieved by using the distributive property of multiplication over addition. The product of an nth degree polynomial can also be represented as a polynomial of degree n + n = 2n.
To find the sum of two nth degree polynomials, combine like terms and simplify the resulting polynomial. To find the product of two nth degree polynomials, use the distributive property of multiplication to multiply each term of one polynomial by each term of the other polynomial, and then combine like terms and simplify the resulting polynomial.
Nth degree polynomials can be used to model various real-life phenomena, such as population growth, stock market trends, and projectile motion. They are also commonly used in engineering and physics to represent complex systems and equations.