Answer :
To factor the expression [tex]\(21x^2 + 70x^4\)[/tex] completely, follow these steps:
1. Identify the Greatest Common Factor (GCF):
Look for the largest factor that both terms share.
- For the coefficients 21 and 70, the GCF is 7.
- For the variable part, both terms have at least [tex]\(x^2\)[/tex].
Therefore, the GCF of the entire expression is [tex]\(7x^2\)[/tex].
2. Factor out the GCF:
Divide each term by the GCF and factor it out of the expression.
[tex]\[
21x^2 + 70x^4 = 7x^2(3) + 7x^2(10x^2)
\][/tex]
This simplifies to:
[tex]\[
7x^2(3 + 10x^2)
\][/tex]
3. Check for further factorization:
Look inside the parentheses to see if [tex]\(3 + 10x^2\)[/tex] can be factored further. In this case, [tex]\(3 + 10x^2\)[/tex] does not factor further over the integers.
So, the completely factored form of the expression is:
[tex]\[
7x^2(10x^2 + 3)
\][/tex]
1. Identify the Greatest Common Factor (GCF):
Look for the largest factor that both terms share.
- For the coefficients 21 and 70, the GCF is 7.
- For the variable part, both terms have at least [tex]\(x^2\)[/tex].
Therefore, the GCF of the entire expression is [tex]\(7x^2\)[/tex].
2. Factor out the GCF:
Divide each term by the GCF and factor it out of the expression.
[tex]\[
21x^2 + 70x^4 = 7x^2(3) + 7x^2(10x^2)
\][/tex]
This simplifies to:
[tex]\[
7x^2(3 + 10x^2)
\][/tex]
3. Check for further factorization:
Look inside the parentheses to see if [tex]\(3 + 10x^2\)[/tex] can be factored further. In this case, [tex]\(3 + 10x^2\)[/tex] does not factor further over the integers.
So, the completely factored form of the expression is:
[tex]\[
7x^2(10x^2 + 3)
\][/tex]
