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Answer :
To factor out the greatest common factor (GCF) from the expression [tex]\(91x^{10} + 39x^5\)[/tex], we will follow these steps:
1. Identify the Coefficient GCF:
- Look at the coefficients of the terms, which are 91 and 39.
- The GCF of 91 and 39 is 13 because 13 is the largest number that divides both 91 and 39 without leaving a remainder.
2. Identify the Variable GCF:
- Look at the variable part of each term, which is [tex]\(x^{10}\)[/tex] and [tex]\(x^5\)[/tex].
- The GCF in terms of the variable [tex]\(x\)[/tex] is [tex]\(x^5\)[/tex] since it's the smallest power of [tex]\(x\)[/tex] present in both terms.
3. Combine the Coefficient and Variable GCF:
- The overall GCF of the entire expression is [tex]\(13x^5\)[/tex].
4. Factor the GCF out of the Expression:
- Divide each term in the expression by [tex]\(13x^5\)[/tex]:
- For the first term: [tex]\(\frac{91x^{10}}{13x^5} = 7x^5\)[/tex]
- For the second term: [tex]\(\frac{39x^5}{13x^5} = 3\)[/tex]
- Therefore, when we factor [tex]\(13x^5\)[/tex] out of the expression, we get:
[tex]\[
13x^5(7x^5 + 3)
\][/tex]
So, the expression [tex]\(91x^{10} + 39x^5\)[/tex] in factored form is [tex]\(13x^5(7x^5 + 3)\)[/tex].
1. Identify the Coefficient GCF:
- Look at the coefficients of the terms, which are 91 and 39.
- The GCF of 91 and 39 is 13 because 13 is the largest number that divides both 91 and 39 without leaving a remainder.
2. Identify the Variable GCF:
- Look at the variable part of each term, which is [tex]\(x^{10}\)[/tex] and [tex]\(x^5\)[/tex].
- The GCF in terms of the variable [tex]\(x\)[/tex] is [tex]\(x^5\)[/tex] since it's the smallest power of [tex]\(x\)[/tex] present in both terms.
3. Combine the Coefficient and Variable GCF:
- The overall GCF of the entire expression is [tex]\(13x^5\)[/tex].
4. Factor the GCF out of the Expression:
- Divide each term in the expression by [tex]\(13x^5\)[/tex]:
- For the first term: [tex]\(\frac{91x^{10}}{13x^5} = 7x^5\)[/tex]
- For the second term: [tex]\(\frac{39x^5}{13x^5} = 3\)[/tex]
- Therefore, when we factor [tex]\(13x^5\)[/tex] out of the expression, we get:
[tex]\[
13x^5(7x^5 + 3)
\][/tex]
So, the expression [tex]\(91x^{10} + 39x^5\)[/tex] in factored form is [tex]\(13x^5(7x^5 + 3)\)[/tex].
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Rewritten by : Jeany
