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]
[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]
