Use (2x^3−3x^2−11x+6)/(x−3)=2x^2+3x−2 to factor 2x^3-3x^2-11x+6 completely.

Key Concepts

Polynomial Division

Polynomial division is a method used to divide one polynomial by another, similar to long division with numbers. In this context, dividing the polynomial 2x^3−3x^2−11x+6 by x−3 allows us to simplify the expression and find the quotient, which is essential for factoring the original polynomial completely.

Factoring Polynomials

Factoring polynomials involves expressing a polynomial as a product of its factors, which can be simpler polynomials or numbers. Understanding how to factor is crucial for solving polynomial equations and simplifying expressions, as it reveals the roots of the polynomial and helps in further analysis.

Remainder Theorem

The Remainder Theorem states that when a polynomial f(x) is divided by (x - c), the remainder of this division is f(c). This theorem is useful for determining whether (x - c) is a factor of the polynomial, as a remainder of zero indicates that c is a root, facilitating the complete factorization of the polynomial.