Factor the expression completely.

Question

48, x, to the power 4 , minus, 18, x, to the power 5
48x
4
−18x
5

Answer 1

To factor the expression \( 48x^4 - 18x^5 \) completely, we can start by identifying the greatest common factor (GCF) of the terms.

1. Identify the GCF:

   • The coefficients are \( 48 \) and \( -18 \). The GCF of \( 48 \) and \( 18 \) is \( 6 \).
   • The variable part involves \( x^4 \) and \( x^5 \). The GCF of \( x^4 \) and \( x^5 \) is \( x^4 \).

   Therefore, the overall GCF of the expression is \( 6x^4 \).

2. Factor out the GCF: \[ 48x^4 - 18x^5 = 6x^4(8 - 3x) \]

3. Check if the remaining expression can be factored further: The remaining expression \( 8 - 3x \) does not factor further as there are no common factors and it is a linear expression.

Thus, the completely factored form of the expression \( 48x^4 - 18x^5 \) is: \[ \boxed{6x^4(8 - 3x)} \]