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Answer :
To factor the expression [tex]\(4x^9 + 2x^6 + 6\)[/tex] completely, we start by identifying the greatest common factor (GCF) of all the terms in the expression.
1. Identify the GCF of the coefficients:
- The coefficients in the expression are 4, 2, and 6.
- The GCF of 4, 2, and 6 is 2.
2. Identify the GCF for the variable terms:
- In this expression, the variable terms are [tex]\(x^9\)[/tex] and [tex]\(x^6\)[/tex].
- The GCF of [tex]\(x^9\)[/tex] and [tex]\(x^6\)[/tex] is [tex]\(x^6\)[/tex].
- However, since the third term, 6, doesn't have a variable part, the overall GCF of the expression is just 2.
3. Factor out the GCF:
- Divide each term in the expression by the GCF (which is 2) and factor it out:
- [tex]\(4x^9 + 2x^6 + 6 = 2(2x^9 + x^6 + 3)\)[/tex].
Therefore, the fully factored expression is [tex]\(2(2x^9 + x^6 + 3)\)[/tex].
1. Identify the GCF of the coefficients:
- The coefficients in the expression are 4, 2, and 6.
- The GCF of 4, 2, and 6 is 2.
2. Identify the GCF for the variable terms:
- In this expression, the variable terms are [tex]\(x^9\)[/tex] and [tex]\(x^6\)[/tex].
- The GCF of [tex]\(x^9\)[/tex] and [tex]\(x^6\)[/tex] is [tex]\(x^6\)[/tex].
- However, since the third term, 6, doesn't have a variable part, the overall GCF of the expression is just 2.
3. Factor out the GCF:
- Divide each term in the expression by the GCF (which is 2) and factor it out:
- [tex]\(4x^9 + 2x^6 + 6 = 2(2x^9 + x^6 + 3)\)[/tex].
Therefore, the fully factored expression is [tex]\(2(2x^9 + x^6 + 3)\)[/tex].
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