In Exercises 1–10, factor out the greatest common factor. 9x^4−18x^3+27x^2

Key Concepts

Greatest Common Factor (GCF)

The Greatest Common Factor is the largest integer or algebraic expression that divides each term of a polynomial without leaving a remainder. To find the GCF, identify the common factors in the coefficients and the variables of each term. For example, in the expression 9x^4, -18x^3, and 27x^2, the GCF is 9x^2, as it is the highest factor that can be factored out from all terms.

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial as a product of its factors. This process simplifies expressions and can make solving equations easier. In the case of the polynomial 9x^4 - 18x^3 + 27x^2, factoring out the GCF allows us to express it in a simpler form, which can then be further analyzed or solved.

Polynomial Terms

Polynomial terms are the individual components of a polynomial, typically expressed in the form ax^n, where 'a' is a coefficient, 'x' is a variable, and 'n' is a non-negative integer exponent. Understanding the structure of polynomial terms is crucial for factoring, as it helps identify common factors and simplifies the polynomial. In the given expression, the terms are 9x^4, -18x^3, and 27x^2.