Question

factor out the greatest common factor.
$18x^{7}-81x^{6}-54x^{5}-28x^{4}$
$?\quad(18x^{3}-81x^{2}-54x-28)$

Explanation:

Step1: Identify GCF of coefficients

The coefficients are 18, 81, 54, 28. The greatest common factor of these numbers is 1, since 28's factors are 1,2,4,7,14,28 and 81 is not divisible by any of these except 1.

Step2: Identify GCF of variables

The variable terms are $x^7$, $x^6$, $x^5$, $x^4$. The lowest exponent of $x$ is 4, so the GCF is $x^4$.

Step3: Combine GCFs

Multiply the GCF of coefficients and variables: $1 \times x^4 = x^4$.
Verify: $x^4(18x^3 - 81x^2 - 54x - 28) = 18x^7 - 81x^6 - 54x^5 - 28x^4$, which matches the original expression.

Answer:

$x^4$