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Answer :
To factor the greatest common factor (GCF) out of the polynomial [tex]\(4x^6 + 12x^4 + 8x^3\)[/tex], follow these steps:
1. Identify the Coefficients: Look at the coefficients of each term in the polynomial. The coefficients are 4, 12, and 8.
2. Find the GCF of the Coefficients: Determine the greatest common factor of the numbers 4, 12, and 8. The GCF of these numbers is 4.
3. Factor Out the GCF: Now that we know the GCF is 4, we can factor 4 out from each term of the polynomial:
- For [tex]\(4x^6\)[/tex], factor out 4 to get [tex]\(x^6\)[/tex].
- For [tex]\(12x^4\)[/tex], factor out 4 to get [tex]\(3x^4\)[/tex].
- For [tex]\(8x^3\)[/tex], factor out 4 to get [tex]\(2x^3\)[/tex].
4. Rewrite the Polynomial: After factoring out the GCF, the polynomial becomes:
[tex]\[
4(x^6 + 3x^4 + 2x^3)
\][/tex]
Thus, the factored form of the polynomial is [tex]\(4(x^6 + 3x^4 + 2x^3)\)[/tex].
1. Identify the Coefficients: Look at the coefficients of each term in the polynomial. The coefficients are 4, 12, and 8.
2. Find the GCF of the Coefficients: Determine the greatest common factor of the numbers 4, 12, and 8. The GCF of these numbers is 4.
3. Factor Out the GCF: Now that we know the GCF is 4, we can factor 4 out from each term of the polynomial:
- For [tex]\(4x^6\)[/tex], factor out 4 to get [tex]\(x^6\)[/tex].
- For [tex]\(12x^4\)[/tex], factor out 4 to get [tex]\(3x^4\)[/tex].
- For [tex]\(8x^3\)[/tex], factor out 4 to get [tex]\(2x^3\)[/tex].
4. Rewrite the Polynomial: After factoring out the GCF, the polynomial becomes:
[tex]\[
4(x^6 + 3x^4 + 2x^3)
\][/tex]
Thus, the factored form of the polynomial is [tex]\(4(x^6 + 3x^4 + 2x^3)\)[/tex].
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