High School

We appreciate your visit to Factor out the greatest common factor from 7x 4 21x 3. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Factor out the greatest common factor from \( 7x^{4} + 21x^{3} \).

Answer :

Final Answer:

The greatest common factor of the expression[tex]\(7x^4 + 21x^3\) is \(7x^3\).[/tex]

Explanation:

To find the greatest common factor (GCF) of [tex]\(7x^4 + 21x^3\),[/tex] we look for the highest power of \(x\) that divides both terms. In this case,[tex]\(7x^3\)[/tex] is the greatest common factor. By factoring out [tex]\(7x^3\)[/tex], we get [tex]\(7x^3(x + 3)\)[/tex]. The process involves dividing each term by [tex]\(7x^3\),[/tex] resulting in the factored form.

The GCF is found by identifying the largest power of the common factor present in both terms. In [tex]\(7x^4 + 21x^3\), \(x^3\)[/tex] is the highest power that divides both terms evenly. Factoring out [tex]\(7x^3\)[/tex] leaves us with the simplified expression [tex]\(7x^3(x + 3)\)[/tex], where [tex]\(x + 3\)[/tex] represents the remaining factor after factoring out the GCF.

This method is essential for simplifying algebraic expressions and equations by factoring out common factors. It allows us to rewrite complex expressions in a more concise form, making it easier to analyze and work with. In this case, factoring out the GCF helps reveal the underlying structure of the expression, making it more manageable for further mathematical operations or analysis.

Thanks for taking the time to read Factor out the greatest common factor from 7x 4 21x 3. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada