Answer :

[tex]21 {x}^{4} + 70x \\ 7x(3 {x}^{3} + 10)[/tex]

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.