Let's start by finding the GCF of 4 and 8.
Factors of4:& 1,2,and 4
Factors of8:& 1,2, 4,and8
We found that the GCF of the coefficients is 4.
Since only one of the terms contains the variable, there are no variables repeated in both terms.
Thus, the GCF of the expression is 4. Now we can write the given expression in terms of the GCF.
4x+8 ⇔ 4* x+ 4* 2
Finally, we will factor out the GCF.
4* x+ 4* 2 ⇔ 4(x+2)
b We want to find the GCF of the terms in the given expression. To do so, we will consider coefficients and variables separately.
10 x+ 25 y+ 5
Let's start by finding the GCF of 10, 25, and 5.
Factors of10:& 1,2, 5,and10
Factors of25:& 1, 5,and25
Factors of5:& 1and 5
We found that the GCF of the coefficients is 5.
Since there are no variables repeated in all three terms, the GCF of the expression is 5. Now we can write the given expression in terms of the GCF.
10x+25y+5
⇕
5* 2x+ 5* 5y+ 5* 1
Finally, we will factor out the GCF.
5* 2x+ 5* 5y+ 5* 1
⇕
5(2x+5y+1)
c We want to find the GCF of the terms in the given expression. To do so, we will consider coefficients and variables separately.
2 x^2- 8 x
Let's start by finding the GCF of 2 and 8.
Factors of2:& 1and 2
Factors of8:& 1, 2,4,and 8
We found that the GCF of the coefficients is 2. To find the GCF of the variables, we need to identify the variables repeated in both terms, and write them with their minimum exponents.
\begin{aligned}
\textbf{Factors of }\bm{1^\text{st}}\textbf{ Variable:}&\ {\color{#FF0000}{x}}, x^2\\
\textbf{Factors of }\bm{2^\text{nd}}\textbf{ Variable:}&\ {\color{#FF0000}{x}}
\end{aligned}
We see that there is one repeated variable factor, x.
Thus, the GCF of the expression is 2* x= 2x. Now we can write the given expression in terms of the GCF.
2x^2-8x ⇔ 2x* x- 2x* 4
Finally, we will factor out the GCF.
2x* x- 2x* 4 ⇔ 2x(x-4)
d We want to find the GCF of the terms in the given expression. To do so, we will consider coefficients and variables separately.
9 x^2y+ 12 x+ 3 xy
Let's start by finding the GCF of 9, 12, and 3.
Factors of9:& 1, 3,and9
Factors of12:& 1,2, 3,4,6,and 12
Factors of3:& 1and 3
We found that the GCF of the coefficients is 3. To find the GCF of the variables, we need to identify the variables repeated in both terms, and write them with their minimum exponents.
\begin{aligned}
\textbf{Factors of }\bm{1^\text{st}}\textbf{ Variable:}&\ {\color{#FF0000}{x}}, x^2, y, xy, x^2y\\
\textbf{Factors of }\bm{2^\text{nd}}\textbf{ Variable:}&\ {\color{#FF0000}{x}}\\
\textbf{Factors of }\bm{3^\text{rd}}\textbf{ Variable:}&\ {\color{#FF0000}{x}}, y, xy
\end{aligned}
We see that there is one repeated variable factor, x.
Thus, the GCF of the expression is 3* x= 3x. Now we can write the given expression in terms of the GCF.
9x^2y+12x+3xy
⇕
3x* 3xy+ 3x* 4+ 3x* y
Finally, we will factor out the GCF.
3x* 3xy+ 3x* 4+ 3x* y
⇕
3x(3xy+4+y)
