Answer :

First, identify the greatest common factor (GCF) of all terms in the expression
[tex]$$30x - 70x^4.$$[/tex]

1. Look at the coefficients: the GCF of 30 and 70 is 10.

2. Look at the variable part: both terms contain at least one factor of [tex]$x$[/tex], so we can factor out [tex]$x$[/tex].

Thus, the overall GCF is [tex]$10x$[/tex].

Next, factor [tex]$10x$[/tex] out of the expression:
[tex]$$30x - 70x^4 = 10x\left(\frac{30x}{10x} - \frac{70x^4}{10x}\right).$$[/tex]

Compute the terms inside the parentheses:
- For the first term:
[tex]$$\frac{30x}{10x} = 3.$$[/tex]
- For the second term:
[tex]$$\frac{70x^4}{10x} = 7x^3.$$[/tex]
Note that the sign remains negative.

So, the factored expression becomes:
[tex]$$10x(3 - 7x^3).$$[/tex]

Thus, the fully factored form of the expression is
[tex]$$\boxed{10x(3 - 7x^3)}.$$[/tex]

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Rewritten by : Barada