Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial. 15n^10+40n^9-5n^8 square

To factor out the greatest common factor from the polynomial \(15n^{10} + 40n^{9} - 5n^{8}\), we first identify the greatest common factor (GCF) of the coefficients and the lowest power of \(n\) in the terms.<br /><br />1. **Identify the GCF of the coefficients:**<br /> - The coefficients are 15, 40, and -5.<br /> - The prime factorizations are:<br /> - \(15 = 3 \times 5\)<br /> - \(40 = 2^3 \times 5\)<br /> - \(-5 = -1 \times 5\)<br /> - The common factor among these is 5.<br /><br />2. **Identify the GCF of the variable terms:**<br /> - The powers of \(n\) are \(n^{10}\), \(n^{9}\), and \(n^{8}\).<br /> - The lowest power of \(n\) is \(n^{8}\).<br /><br />3. **Combine the GCF of the coefficients and the variable terms:**<br /> - The GCF of the polynomial is \(5n^{8}\).<br /><br />4. **Factor out the GCF from each term:**<br /> - \(15n^{10} = 5n^{8} \cdot 3n^{2}\)<br /> - \(40n^{9} = 5n^{8} \cdot 8n\)<br /> - \(-5n^{8} = 5n^{8} \cdot (-1)\)<br /><br />5. **Write the factored form:**<br /> - \(15n^{10} + 40n^{9} - 5n^{8} = 5n^{8}(3n^{2} + 8n - 1)\)<br /><br />So, the factored form of the polynomial is:<br />\[ 5n^{8}(3n^{2} + 8n - 1) \]