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Chapter 0: Problem 6

Factor out the greatest common factor. $$6 x^{4}-18 x^{3}+12 x^{2}$$

Short Answer

Expert verified
The factorized form of the polynomial \(6 x^{4}-18 x^{3}+12 x^{2}\) is \(6x^2(x^2 - 3x + 2)\).

Step by step solution

01

Identifying the GCF

For \(6 x^{4}\), \(18 x^{3}\), and \(12 x^{2}\), the GCF is \(6x^2\). You can find this by examining each term: Both 6 and 18 are divisible by 6, and all three terms have at least two factors of x.
02

Factorization

Factor out \(6x^2\) from each term. The process follows the rule \(A(B + C) = AB + AC\).
03

Simplifying each term

\(6x^2(1*x^2 - 3*x + 2)\). Simplify each term by dividing by the GCF. This gives us \(x^2 - 3x + 2\) after factorization.

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