Problem 39 - Introductory Algebra for College Students

Question

Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$10 x-20 x^{2}+5 x^{3}$$

Step-by-Step Solution

Answer

The factored form of the given polynomial is \(5x(2 - 4x + x^{2})\).

Step 1: Identifying the greatest common factor

Check each term of the polynomial \(10x - 20x^{2} + 5x^{3}\). It's observed that the greatest common factor of all the terms is \(5x\).

Step 2: Factoring out the greatest common factor

Pulling out the common factor, we get \(5x(2 - 4x + x^{2})\).

Step 3: Check if the factored expression can be factored further

In the factored expression \(5x(2 - 4x + x^{2})\), the polynomial inside the parentheses cannot be factored further since there is no common factor in the terms and it does not meet any special factoring forms.