What is the greastest common factor of the following polynomial: -35m^5+56 GCF: square

To find the greatest common factor (GCF) of the polynomial \(-35m^5 + 56\), we need to determine the GCF of the coefficients and the GCF of the variable terms.<br /><br />1. **Coefficients:**<br /> - The coefficients are \(-35\) and \(56\).<br /> - The prime factorization of \(-35\) is \( -1 \times 5 \times 7 \).<br /> - The prime factorization of \(56\) is \( 2^3 \times 7 \).<br /><br /> The common prime factor is \(7\).<br /><br />2. **Variable Terms:**<br /> - The variable term in the polynomial is \(m^5\).<br /> - Since there is no other variable term in the polynomial, the GCF of the variable terms is simply \(m^0 = 1\).<br /><br />Combining these, the GCF of the polynomial \(-35m^5 + 56\) is the product of the GCF of the coefficients and the GCF of the variable terms:<br /><br />\[ \text{GCF} = 7 \times 1 = 7 \]<br /><br />Thus, the greatest common factor of the polynomial \(-35m^5 + 56\) is \(\boxed{7}\).