Answer :
To factor the expression [tex]\(21x^4 + 70x\)[/tex] completely, follow these steps:
1. Identify the Greatest Common Factor (GCF):
Look for the greatest common factor of the terms. Both terms, [tex]\(21x^4\)[/tex] and [tex]\(70x\)[/tex], are divisible by 7 and contain the variable [tex]\(x\)[/tex].
2. Factor Out the GCF:
The greatest common factor here is [tex]\(7x\)[/tex]. Factor [tex]\(7x\)[/tex] out from each term in the expression:
[tex]\[
21x^4 + 70x = 7x(3x^3 + 10)
\][/tex]
3. Verify Your Factoring:
To ensure the factorization is correct, you can expand [tex]\(7x(3x^3 + 10)\)[/tex] back:
[tex]\[
7x \times 3x^3 = 21x^4
\][/tex]
[tex]\[
7x \times 10 = 70x
\][/tex]
Combining these, you get back to the original expression [tex]\(21x^4 + 70x\)[/tex].
The completely factored form of the expression is [tex]\(\boxed{7x(3x^3 + 10)}\)[/tex].
1. Identify the Greatest Common Factor (GCF):
Look for the greatest common factor of the terms. Both terms, [tex]\(21x^4\)[/tex] and [tex]\(70x\)[/tex], are divisible by 7 and contain the variable [tex]\(x\)[/tex].
2. Factor Out the GCF:
The greatest common factor here is [tex]\(7x\)[/tex]. Factor [tex]\(7x\)[/tex] out from each term in the expression:
[tex]\[
21x^4 + 70x = 7x(3x^3 + 10)
\][/tex]
3. Verify Your Factoring:
To ensure the factorization is correct, you can expand [tex]\(7x(3x^3 + 10)\)[/tex] back:
[tex]\[
7x \times 3x^3 = 21x^4
\][/tex]
[tex]\[
7x \times 10 = 70x
\][/tex]
Combining these, you get back to the original expression [tex]\(21x^4 + 70x\)[/tex].
The completely factored form of the expression is [tex]\(\boxed{7x(3x^3 + 10)}\)[/tex].
