What is the basic principle that can be used to simplify a polynomial?
Your school subject is math -- not college.
Most polynomials can factored into a product of lower-order polynomials.
The basic principle that can be used to simplify a polynomial is combining like terms.
To simplify a polynomial, you need to combine the terms that have the same variable raised to the same exponent. Let's take an example to understand this process.
Consider the polynomial: 3x^2 + 2x - 5x^2 - 4x + 7
Step 1: Arrange the terms in descending order of the exponents.
-5x^2 + 3x^2 + 2x - 4x + 7
Step 2: Combine the like terms.
(-5x^2 + 3x^2) + (2x - 4x) + 7
-2x^2 - 2x + 7
In this example, we combined the like terms "-5x^2" and "3x^2" to get "-2x^2". We also combined the like terms "2x" and "-4x" to get "-2x". The constant term "7" remains unchanged as it has no like terms to combine with.
So, by combining like terms, we simplified the original polynomial to the simplified form -2x^2 - 2x + 7.