Factor 5p-45
Understand the Problem
The question is asking to factor the given expression. We can factor out the greatest common factor (GCF) from both terms.
Answer
$8x^2(2x^3 + 3)$
Answer for screen readers
$8x^2(2x^3 + 3)$
Steps to Solve
- Identify the coefficients and variables in each term
The given expression is $16x^5 + 24x^2$. The first term is $16x^5$ and the second term is $24x^2$.
- Find the greatest common factor (GCF) of the coefficients
The coefficients are 16 and 24. The factors of 16 are 1, 2, 4, 8, and 16. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The greatest common factor of 16 and 24 is 8.
- Find the greatest common factor of the variables
The variables are $x^5$ and $x^2$. The greatest common factor of $x^5$ and $x^2$ is $x^2$ (since $x^2$ is the lowest power of $x$ in both terms).
- Determine the overall greatest common factor
The greatest common factor (GCF) of the entire expression is the product of the GCF of the coefficients and the GCF of the variables, which is $8x^2$.
- Factor out the GCF from each term
Divide each term in the original expression by the GCF $8x^2$:
$\frac{16x^5}{8x^2} = 2x^3$
$\frac{24x^2}{8x^2} = 3$
- Write the factored expression
Write the GCF outside the parentheses, and the result of the division inside the parentheses: $8x^2(2x^3 + 3)$
$8x^2(2x^3 + 3)$
More Information
Factoring out the greatest common factor is a very useful skill in algebra. It helps simplify expressions and solve equations.
Tips
A common mistake is to only factor out the variable or the coefficient, but not both. Remember to find the greatest common factor of both the coefficients and the variables. Another common mistake is to incorrectly divide the terms when factoring out the GCF.
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