Questionexpression completely. $-60 x^{4}+54 x$

Studdy Solution

STEP 1

1. The expression $-60x^4 + 54x$ can be factored completely.
2. We will look for common factors and apply factoring techniques to simplify the expression.

STEP 2

1. Identify and factor out the greatest common factor (GCF) from the expression.
2. Simplify the expression by factoring any remaining polynomial.

STEP 3

Identify the greatest common factor (GCF) of the terms $-60x^4$ and $54x$ .
- The coefficients are $-60$ and $54$ . The GCF of these numbers is $6$ . - The variable part is $x^4$ and $x$ . The GCF of these is $x$ .
Thus, the GCF of the entire expression is $6x$ .
Factor out the GCF:
$-60x^4 + 54x = 6x(-10x^3 + 9)$

STEP 4

Check if the expression inside the parentheses, $-10x^3 + 9$ , can be factored further.
- The expression $-10x^3 + 9$ is a simple polynomial with no common factors or recognizable patterns for further factoring.
Thus, the expression is factored completely as:
$6x(-10x^3 + 9)$

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