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What is the greatest common factor of [tex]$14x^3 - 21x$[/tex]?

A. [tex]$7x^2$[/tex]
B. [tex][tex]$7x$[/tex][/tex]
C. [tex]$14x^3$[/tex]
D. [tex]$7x^3$[/tex]

Answer :

To find the greatest common factor (GCF) of the polynomial

[tex]$$14x^3 - 21x,$$[/tex]

we proceed as follows:

1. Identify the common numerical factor:
The coefficients in the expression are 14 and -21. The greatest common divisor of 14 and 21 is 7.

2. Identify the common variable factor:
The variable [tex]$x$[/tex] appears in both terms, and the powers are [tex]$x^3$[/tex] and [tex]$x$[/tex]. The smallest power present is [tex]$x^1$[/tex], which is simply [tex]$x$[/tex].

3. Combine the common factors:
Multiply the common numerical factor and the common variable factor to get

[tex]$$7 \cdot x = 7x.$$[/tex]

Thus, the greatest common factor of the polynomial is

[tex]$$\boxed{7x}.$$[/tex]

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