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Answer :
To factor the greatest common factor (GCF) out of the expression [tex]\(91 x^{10} + 39 x^5\)[/tex], follow these steps:
1. Identify the coefficients and their GCF:
- The coefficients of the terms are 91 and 39.
- To find the GCF of 91 and 39, list their prime factorizations:
- 91 = [tex]\(7 \times 13\)[/tex]
- 39 = [tex]\(3 \times 13\)[/tex]
- The common factor in these prime factorizations is 13. So, the GCF of 91 and 39 is 13.
2. Identify the variable part:
- The terms [tex]\(x^{10}\)[/tex] and [tex]\(x^5\)[/tex] have the variable [tex]\(x\)[/tex].
- The smallest power of [tex]\(x\)[/tex] in the expression is [tex]\(x^5\)[/tex].
3. Combine the GCF of the coefficients and the variable part:
- The GCF of the expression [tex]\(91 x^{10} + 39 x^5\)[/tex] is [tex]\(13x^5\)[/tex].
4. Factor out the GCF from each term:
- Divide each term by the GCF [tex]\(13 x^5\)[/tex]:
[tex]\[
\frac{91 x^{10}}{13 x^5} = 7 x^5
\][/tex]
[tex]\[
\frac{39 x^5}{13 x^5} = 3
\][/tex]
5. Write the factored form:
- Using the GCF [tex]\(13 x^5\)[/tex], factor the expression:
[tex]\[
91 x^{10} + 39 x^5 = 13 x^5 (7 x^5 + 3)
\][/tex]
Therefore, the expression [tex]\(91 x^{10} + 39 x^5\)[/tex] factored with its GCF is:
[tex]\[
13 x^5 (7 x^5 + 3)
\][/tex]
1. Identify the coefficients and their GCF:
- The coefficients of the terms are 91 and 39.
- To find the GCF of 91 and 39, list their prime factorizations:
- 91 = [tex]\(7 \times 13\)[/tex]
- 39 = [tex]\(3 \times 13\)[/tex]
- The common factor in these prime factorizations is 13. So, the GCF of 91 and 39 is 13.
2. Identify the variable part:
- The terms [tex]\(x^{10}\)[/tex] and [tex]\(x^5\)[/tex] have the variable [tex]\(x\)[/tex].
- The smallest power of [tex]\(x\)[/tex] in the expression is [tex]\(x^5\)[/tex].
3. Combine the GCF of the coefficients and the variable part:
- The GCF of the expression [tex]\(91 x^{10} + 39 x^5\)[/tex] is [tex]\(13x^5\)[/tex].
4. Factor out the GCF from each term:
- Divide each term by the GCF [tex]\(13 x^5\)[/tex]:
[tex]\[
\frac{91 x^{10}}{13 x^5} = 7 x^5
\][/tex]
[tex]\[
\frac{39 x^5}{13 x^5} = 3
\][/tex]
5. Write the factored form:
- Using the GCF [tex]\(13 x^5\)[/tex], factor the expression:
[tex]\[
91 x^{10} + 39 x^5 = 13 x^5 (7 x^5 + 3)
\][/tex]
Therefore, the expression [tex]\(91 x^{10} + 39 x^5\)[/tex] factored with its GCF is:
[tex]\[
13 x^5 (7 x^5 + 3)
\][/tex]
Thank you for reading the article Factor the GCF out of the following expression and write your answer in factored form tex 91x 10 39x 5 tex. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
