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Answer :
To find the greatest common factor (GCF) of the expressions
[tex]$$
7x^5,\quad 35x^2,\quad \text{and} \quad 70x,
$$[/tex]
we can follow these steps:
1. Identify the Coefficients:
The coefficients in the expressions are:
[tex]$$
7, \; 35, \; \text{and} \; 70.
$$[/tex]
The greatest common factor of these numbers is [tex]$7$[/tex].
2. Identify the Powers of [tex]$x$[/tex]:
The powers of [tex]$x$[/tex] in each expression are:
[tex]$$
x^5,\; x^2,\; \text{and} \; x^1.
$$[/tex]
For the variable part, we look for the smallest exponent. Since the exponents are [tex]$5$[/tex], [tex]$2$[/tex], and [tex]$1$[/tex], the smallest is [tex]$1$[/tex], which means the common factor from the variable part is [tex]$x^1 = x$[/tex].
3. Combine the Factors:
Multiplying the GCF of the coefficients with the common variable factor gives:
[tex]$$
7 \times x = 7x.
$$[/tex]
Thus, the greatest common factor of the three expressions is
[tex]$$
\boxed{7x}.
$$[/tex]
[tex]$$
7x^5,\quad 35x^2,\quad \text{and} \quad 70x,
$$[/tex]
we can follow these steps:
1. Identify the Coefficients:
The coefficients in the expressions are:
[tex]$$
7, \; 35, \; \text{and} \; 70.
$$[/tex]
The greatest common factor of these numbers is [tex]$7$[/tex].
2. Identify the Powers of [tex]$x$[/tex]:
The powers of [tex]$x$[/tex] in each expression are:
[tex]$$
x^5,\; x^2,\; \text{and} \; x^1.
$$[/tex]
For the variable part, we look for the smallest exponent. Since the exponents are [tex]$5$[/tex], [tex]$2$[/tex], and [tex]$1$[/tex], the smallest is [tex]$1$[/tex], which means the common factor from the variable part is [tex]$x^1 = x$[/tex].
3. Combine the Factors:
Multiplying the GCF of the coefficients with the common variable factor gives:
[tex]$$
7 \times x = 7x.
$$[/tex]
Thus, the greatest common factor of the three expressions is
[tex]$$
\boxed{7x}.
$$[/tex]
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