What is the greastest tcommon factor of the following polynomial: 9n^3+6n^2-10n GCP: typeyouranswer

To find the greatest common factor (GCF) of the polynomial \(9n^3 + 6n^2 - 10n\), we need to identify the largest factor that divides each term of the polynomial.<br /><br />First, let's factor each term individually:<br /><br />1. \(9n^3\):<br /> \[<br /> 9n^3 = 3^2 \cdot n^3<br /> \]<br /><br />2. \(6n^2\):<br /> \[<br /> 6n^2 = 2 \cdot 3 \cdot n^2<br /> \]<br /><br />3. \(-10n\):<br /> \[<br /> -10n = -1 \cdot 2 \cdot 5 \cdot n<br /> \]<br /><br />Next, we identify the common factors in each term:<br /><br />- The term \(9n^3\) has factors \(3^2 \cdot n^3\).<br />- The term \(6n^2\) has factors \(2 \cdot 3 \cdot n^2\).<br />- The term \(-10n\) has factors \(2 \cdot 5 \cdot n\).<br /><br />The common factors among all three terms are:<br />- The factor \(n\).<br /><br />Therefore, the greatest common factor of the polynomial \(9n^3 + 6n^2 - 10n\) is \(n\).<br /><br />So, the GCF is:<br />\[<br />\boxed{n}<br />\]