Answer :
To find the greatest common factor (GCF) of the polynomial [tex]\(4x^6 - 16x^5 - 12x^4\)[/tex], we need to identify the greatest factor that divides each term of the polynomial.
Let's break it down step by step:
1. Identify the Coefficients:
- The coefficients of the terms are 4, -16, and -12.
2. Find the GCF of the Coefficients:
- The GCF of 4, 16, and 12 can be found by identifying the largest number that divides all three.
- The factors of 4 are 1, 2, 4.
- The factors of 16 are 1, 2, 4, 8, 16.
- The factors of 12 are 1, 2, 3, 4, 6, 12.
- The greatest common factor among these is 4.
3. Identify the Variable Parts:
- The terms have [tex]\(x^6\)[/tex], [tex]\(x^5\)[/tex], and [tex]\(x^4\)[/tex]. We use the lowest power of x common to all terms.
- The lowest power is [tex]\(x^4\)[/tex].
4. Combine the GCF of the Coefficients and Variables:
- So, the GCF of the polynomial is [tex]\(4x^4\)[/tex].
Therefore, the greatest common factor of the polynomial [tex]\(4x^6 - 16x^5 - 12x^4\)[/tex] is [tex]\(4x^4\)[/tex]. Thus, the correct answer is:
B. [tex]\(4x^4\)[/tex]
Let's break it down step by step:
1. Identify the Coefficients:
- The coefficients of the terms are 4, -16, and -12.
2. Find the GCF of the Coefficients:
- The GCF of 4, 16, and 12 can be found by identifying the largest number that divides all three.
- The factors of 4 are 1, 2, 4.
- The factors of 16 are 1, 2, 4, 8, 16.
- The factors of 12 are 1, 2, 3, 4, 6, 12.
- The greatest common factor among these is 4.
3. Identify the Variable Parts:
- The terms have [tex]\(x^6\)[/tex], [tex]\(x^5\)[/tex], and [tex]\(x^4\)[/tex]. We use the lowest power of x common to all terms.
- The lowest power is [tex]\(x^4\)[/tex].
4. Combine the GCF of the Coefficients and Variables:
- So, the GCF of the polynomial is [tex]\(4x^4\)[/tex].
Therefore, the greatest common factor of the polynomial [tex]\(4x^6 - 16x^5 - 12x^4\)[/tex] is [tex]\(4x^4\)[/tex]. Thus, the correct answer is:
B. [tex]\(4x^4\)[/tex]
