Answer :
To find the Greatest Common Factor (GCF) of the terms in the polynomial [tex]\(34x^5 + 12x^6\)[/tex], we need to look at both the coefficients and the variable parts separately.
1. Find the GCF of the coefficients:
- The coefficients are 34 and 12.
- The factors of 34 are 1, 2, 17, and 34.
- The factors of 12 are 1, 2, 3, 4, 6, and 12.
- The largest common factor between them is 2.
2. Find the GCF of the variable parts:
- The variable part of the first term is [tex]\(x^5\)[/tex].
- The variable part of the second term is [tex]\(x^6\)[/tex].
- The GCF of [tex]\(x^5\)[/tex] and [tex]\(x^6\)[/tex] is determined by the lowest power of [tex]\(x\)[/tex] common to both, which is [tex]\(x^5\)[/tex].
3. Combine the GCF of the coefficients and the variable parts:
- The overall GCF is the product of the GCF of the coefficients and the GCF of the variable parts:
[tex]\[
\text{GCF} = 2 \times x^5 = 2x^5
\][/tex]
Therefore, the GCF of the terms in the polynomial [tex]\(34x^5 + 12x^6\)[/tex] is [tex]\(2x^5\)[/tex].
1. Find the GCF of the coefficients:
- The coefficients are 34 and 12.
- The factors of 34 are 1, 2, 17, and 34.
- The factors of 12 are 1, 2, 3, 4, 6, and 12.
- The largest common factor between them is 2.
2. Find the GCF of the variable parts:
- The variable part of the first term is [tex]\(x^5\)[/tex].
- The variable part of the second term is [tex]\(x^6\)[/tex].
- The GCF of [tex]\(x^5\)[/tex] and [tex]\(x^6\)[/tex] is determined by the lowest power of [tex]\(x\)[/tex] common to both, which is [tex]\(x^5\)[/tex].
3. Combine the GCF of the coefficients and the variable parts:
- The overall GCF is the product of the GCF of the coefficients and the GCF of the variable parts:
[tex]\[
\text{GCF} = 2 \times x^5 = 2x^5
\][/tex]
Therefore, the GCF of the terms in the polynomial [tex]\(34x^5 + 12x^6\)[/tex] is [tex]\(2x^5\)[/tex].
