Problem

Reduce the polynomial \(3x^4 - 2x^3 + 4x^2 - 5x + 2\) by factoring out the greatest common factor.

Answer

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Answer

As the greatest common factor is 1, the reduced form of the polynomial is the same as the original polynomial, \(3x^4 - 2x^3 + 4x^2 - 5x + 2\).

Steps

Step 1 ：Identify the greatest common factor of all the terms of the polynomial, which is 1.

Step 2 ：Factor out the greatest common factor from each term of the polynomial. The factored form of the polynomial is \(1(3x^4 - 2x^3 + 4x^2 - 5x + 2)\).

Step 3 ：As the greatest common factor is 1, the reduced form of the polynomial is the same as the original polynomial, \(3x^4 - 2x^3 + 4x^2 - 5x + 2\).

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