Answer :
To factor the greatest common factor (GCF) from the polynomial [tex]\(7x^6 - 28x^4\)[/tex], follow these steps:
1. Identify the GCF of the coefficients:
- The coefficients are 7 and 28. The GCF of 7 and 28 is 7 because 7 is the largest number that divides both 7 and 28 without leaving a remainder.
2. Identify the GCF for the variable terms:
- The polynomial terms are [tex]\(x^6\)[/tex] and [tex]\(x^4\)[/tex]. The GCF of [tex]\(x^6\)[/tex] and [tex]\(x^4\)[/tex] is [tex]\(x^4\)[/tex]. This is because [tex]\(x^4\)[/tex] is the highest power of [tex]\(x\)[/tex] that can be factored out from both terms.
3. Combine the GCF of coefficients and variables:
- The overall GCF of the polynomial [tex]\(7x^6 - 28x^4\)[/tex] is [tex]\(7x^4\)[/tex].
4. Factor out the GCF from each term:
- When you factor [tex]\(7x^4\)[/tex] out of the first term [tex]\(7x^6\)[/tex], you get [tex]\(x^2\)[/tex] because [tex]\(7x^6 \div 7x^4 = x^2\)[/tex].
- When you factor [tex]\(7x^4\)[/tex] out of the second term [tex]\(-28x^4\)[/tex], you get [tex]\(-4\)[/tex] because [tex]\(-28x^4 \div 7x^4 = -4\)[/tex].
5. Write the factored expression:
- After factoring out [tex]\(7x^4\)[/tex], the polynomial becomes [tex]\(7x^4(x^2 - 4)\)[/tex].
Thus, the correct factored form of the polynomial [tex]\(7x^6 - 28x^4\)[/tex] is [tex]\(7x^4(x^2 - 4)\)[/tex].
1. Identify the GCF of the coefficients:
- The coefficients are 7 and 28. The GCF of 7 and 28 is 7 because 7 is the largest number that divides both 7 and 28 without leaving a remainder.
2. Identify the GCF for the variable terms:
- The polynomial terms are [tex]\(x^6\)[/tex] and [tex]\(x^4\)[/tex]. The GCF of [tex]\(x^6\)[/tex] and [tex]\(x^4\)[/tex] is [tex]\(x^4\)[/tex]. This is because [tex]\(x^4\)[/tex] is the highest power of [tex]\(x\)[/tex] that can be factored out from both terms.
3. Combine the GCF of coefficients and variables:
- The overall GCF of the polynomial [tex]\(7x^6 - 28x^4\)[/tex] is [tex]\(7x^4\)[/tex].
4. Factor out the GCF from each term:
- When you factor [tex]\(7x^4\)[/tex] out of the first term [tex]\(7x^6\)[/tex], you get [tex]\(x^2\)[/tex] because [tex]\(7x^6 \div 7x^4 = x^2\)[/tex].
- When you factor [tex]\(7x^4\)[/tex] out of the second term [tex]\(-28x^4\)[/tex], you get [tex]\(-4\)[/tex] because [tex]\(-28x^4 \div 7x^4 = -4\)[/tex].
5. Write the factored expression:
- After factoring out [tex]\(7x^4\)[/tex], the polynomial becomes [tex]\(7x^4(x^2 - 4)\)[/tex].
Thus, the correct factored form of the polynomial [tex]\(7x^6 - 28x^4\)[/tex] is [tex]\(7x^4(x^2 - 4)\)[/tex].
