Factor the expression completely: 30 + 3x^5.
Understand the Problem
The question is asking to factor the algebraic expression completely, which involves finding the common factors in the given expression.
Answer
The completely factored expression is $3(10 + x^5)$.
Answer for screen readers
The completely factored form of the expression is: $$ 3(10 + x^5) $$
Steps to Solve
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Identify the common factor First, we need to look for a common factor in both terms of the expression $30 + 3x^5$. The coefficients are 30 and 3. The greatest common factor (GCF) of these numbers is 3.
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Factor out the common factor Next, we will factor out the GCF from the expression. We rewrite the expression as: $$ 30 + 3x^5 = 3(10 + x^5) $$
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Check if further factoring is possible Now, we check if the expression inside the parentheses, $10 + x^5$, can be factored further. Since $10$ is not a perfect square and $x^5$ does not combine with it in a special way, this expression cannot be factored further.
The completely factored form of the expression is: $$ 3(10 + x^5) $$
More Information
This factoring involves finding the greatest common factor (GCF) of the terms in the expression. Factoring helps simplify polynomial expressions and can be useful in solving equations or analyzing functions.
Tips
- Forgetting to factor out the GCF.
- Attempting to factor the expression inside the parentheses when it cannot be factored further.
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