Questions: Factor the following polynomial completely using the greatest common factor. If the expression cannot be factored, enter the expression as is. 64 s^7 t-40 s^5 t^3

Solution Steps

To factor the given polynomial completely using the greatest common factor (GCF), we need to:

1. Identify the GCF of the coefficients (64 and -40).
2. Identify the GCF of the variable parts (\(s^7\) and \(s^5\)).
3. Identify the GCF of the variable parts (\(t\) and \(t^3\)).
4. Factor out the GCF from the polynomial.

We start with the polynomial: \[ 64 s^{7} t - 40 s^{5} t^{3} \]

To factor the polynomial, we first determine the GCF of the coefficients and the variable parts:

• The GCF of the coefficients \(64\) and \(-40\) is \(8\).
• The GCF of \(s^{7}\) and \(s^{5}\) is \(s^{5}\).
• The GCF of \(t\) and \(t^{3}\) is \(t\).

Thus, the overall GCF is: \[ 8 s^{5} t \]

We can now factor out the GCF from the polynomial: \[ 64 s^{7} t - 40 s^{5} t^{3} = 8 s^{5} t (8 s^{2} - 5 t^{2}) \]

Final Answer