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Answer :
Final answer:
The expression '21[tex]x^4[/tex] + 70x' is factored by first finding the greatest common factor, which is '7x', resulting in the fully factored form '7x(3[tex]x^3[/tex] + 10)'.
Explanation:
To factor the expression 21[tex]x^4[/tex] + 70x completely, you first need to identify the greatest common factor (GCF) that both terms share. In this case, both terms have a factor of x and the number 7. Since 7 goes into 21 three times and into 70 ten times, the GCF is 7x.
Once we extract the GCF, the factored form is:
7x(3[tex]x^3[/tex] + 10)
This expression cannot be factored further since 3[tex]x^3[/tex] and 10 do not have any additional common factors and the trinomial does not factor over the integers.
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