Answer :
To determine the greatest common factor (GCF) of the terms of the polynomial [tex]\(9x^4 + 15x^3 + 21x^2\)[/tex], we need to follow a step-by-step process.
1. Identify the Coefficients: The polynomial given is [tex]\(9x^4 + 15x^3 + 21x^2\)[/tex]. The coefficients of the terms are 9, 15, and 21.
2. Calculate the GCF of the Coefficients:
- The factors of 9 are 1, 3, 9.
- The factors of 15 are 1, 3, 5, 15.
- The factors of 21 are 1, 3, 7, 21.
- The greatest common factor of 9, 15, and 21 is 3, as it is the largest number that divides all three coefficients.
3. Determine the Common Variable Factor:
- Each term has [tex]\(x\)[/tex] raised to some power.
- The powers of [tex]\(x\)[/tex] in the terms are 4, 3, and 2.
- The smallest power of [tex]\(x\)[/tex] among the terms is [tex]\(x^2\)[/tex].
- Therefore, [tex]\(x^2\)[/tex] is the highest power of [tex]\(x\)[/tex] that can be factored out from all terms.
4. Combine the GCF of Coefficients and the Common Variable Factor:
- The GCF of the coefficients is 3.
- The common variable factor is [tex]\(x^2\)[/tex].
- Combining these, we get the greatest common factor of the polynomial [tex]\(9x^4 + 15x^3 + 21x^2\)[/tex].
Therefore, the greatest common factor (GCF) of the terms of the polynomial [tex]\(9x^4 + 15x^3 + 21x^2\)[/tex] is [tex]\(3x^2\)[/tex].
### Answer:
The greatest common factor of the terms of the polynomial [tex]\(9x^4 + 15x^3 + 21x^2\)[/tex] is [tex]\(3x^2\)[/tex].
1. Identify the Coefficients: The polynomial given is [tex]\(9x^4 + 15x^3 + 21x^2\)[/tex]. The coefficients of the terms are 9, 15, and 21.
2. Calculate the GCF of the Coefficients:
- The factors of 9 are 1, 3, 9.
- The factors of 15 are 1, 3, 5, 15.
- The factors of 21 are 1, 3, 7, 21.
- The greatest common factor of 9, 15, and 21 is 3, as it is the largest number that divides all three coefficients.
3. Determine the Common Variable Factor:
- Each term has [tex]\(x\)[/tex] raised to some power.
- The powers of [tex]\(x\)[/tex] in the terms are 4, 3, and 2.
- The smallest power of [tex]\(x\)[/tex] among the terms is [tex]\(x^2\)[/tex].
- Therefore, [tex]\(x^2\)[/tex] is the highest power of [tex]\(x\)[/tex] that can be factored out from all terms.
4. Combine the GCF of Coefficients and the Common Variable Factor:
- The GCF of the coefficients is 3.
- The common variable factor is [tex]\(x^2\)[/tex].
- Combining these, we get the greatest common factor of the polynomial [tex]\(9x^4 + 15x^3 + 21x^2\)[/tex].
Therefore, the greatest common factor (GCF) of the terms of the polynomial [tex]\(9x^4 + 15x^3 + 21x^2\)[/tex] is [tex]\(3x^2\)[/tex].
### Answer:
The greatest common factor of the terms of the polynomial [tex]\(9x^4 + 15x^3 + 21x^2\)[/tex] is [tex]\(3x^2\)[/tex].
