Question

Factor out the greatest common factor: 3x^8 - 27x^7 + 6x^6.

Answer 1

The greatest common factor (GCF) of the expression
`\(3x^8 - 27x^7 + 6x^6\) is \(3x^6\).` Factoring out the GCF results in
`\(3x^6(x^2 - 9x + 2)\).`

Step-by-step explanation:

To find the GCF, identify the common factors in each term. In this expression,
`\(3x^6\)` is the largest common factor, as it can be evenly divided into each term.

The factoring process involves dividing each term by the GCF. Starting with
`(3x^8)`, dividing by
`\(3x^6\)` gives
`\(x^2\).` For
`\(-27x^7\),` dividing by
`\(3x^6\)` gives
`\(-9x\),` and for
`\(6x^6\)`, dividing by
`\(3x^6\)` gives (2).

After factoring out
`\(3x^6\)`, the expression becomes
`(3x^6(x^2 - 9x + 2)).`This factored form represents the original expression, and the GCF has been successfully factored out.