Factor the expression completely: x^3 + x^5y^4.
Understand the Problem
The question is asking to factor the given algebraic expression completely, which involves identifying common factors in the terms of the expression.
Answer
The expression factors to $x^3(1 + x^2y^4)$.
Answer for screen readers
The completely factored form of the expression is: $$ x^3(1 + x^2y^4) $$
Steps to Solve
- Identify Common Factors
First, we look for the common factor in the terms $x^3$ and $x^5y^4$. The common factor here is $x^3$.
- Factor Out the Common Factor
Next, we factor $x^3$ out of both terms: $$ x^3 + x^5y^4 = x^3(1 + x^2y^4) $$
- Check for Further Factorization
We need to check if the remaining expression $1 + x^2y^4$ can be factored further. Since it is a sum of terms without common factors or recognizable patterns, it cannot be factored further.
The completely factored form of the expression is: $$ x^3(1 + x^2y^4) $$
More Information
Factoring is an important skill in algebra that allows you to simplify expressions and solve equations more easily. Identifying common factors is often the first step in factoring polynomials.
Tips
- Failing to identify the greatest common factor. Always check for the highest degree of each variable in the expression.
- Overlooking the possibility of factoring the remaining expression further when applicable.
