Question

Factor each polynomial completely. $$ 2 x^{2}-18 x+36 $$

   Factor each polynomial completely.
$$
2 x^{2}-18 x+36
$$

Trigonometry

David I. Schneider;… 12th Edition

Chapter 0, Problem 78

Instant Answer

Solved by Expert Nick Johnson

02/17/2023

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This gives us: $$ 2(x^{2}-9x+18) $$ Show more…

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Factor each polynomial completely. $$ 2 x^{2}-18 x+36 $$

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Key Concepts

Polynomial Factoring

Polynomial factoring is the process of rewriting a polynomial expression as a product of simpler polynomials or factors. This technique is essential for simplifying expressions, solving equations, and analyzing polynomial functions. It involves identifying patterns and structures within the polynomial that allow for its decomposition into products of lower-degree polynomials.

Greatest Common Factor

The greatest common factor (GCF) is the largest factor that divides all the terms of a polynomial without a remainder. Extracting the GCF is usually the first step in factoring because it simplifies the expression by reducing each term and making further factorization steps more apparent.

Quadratic Factoring

Quadratic factoring refers to breaking down a quadratic polynomial, typically in the form ax^2 + bx + c, into a product of two linear factors. Understanding the relationship between the coefficients and using techniques such as splitting the middle term or applying the quadratic formula are key strategies in efficiently factoring quadratics.

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