High School

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------------------------------------------------ Factor the expression completely:

[tex] 21x^4 + 70x [/tex]

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].