Try to think of the GCF between the coefficients and the GCF between the variables separately.
4x(3x+1)
Practice makes perfect
We want to find the greatest common factor — GCF — of the terms in the given expression. To do so, we will consider coefficients and variables separately.
12 x^2+ 4 x
Let's start by finding the GCF of 12 and 4.
Factors of12:& 1, 2, 3, 4, 6, and12
Factors of4:& 1,2, 4
We found that the GCF of the coefficients is 4. To find the GCF of the variables, we need to identify the variables repeated in both terms, and write them with their minimum exponents.
1^(st)Term Variable Factors:& x, x^2
2^(nd)Term Variable Factors:& x
We see that there is one repeated variable factor. Its minimum exponent is x^1= x.
Thus, the GCF of the expression is 4* x= 4x. Now we can write the given expression in terms of the GCF.
12x^2+4x ⇔ 4x* 3x+ 4x* 1
Finally, we will factor out the GCF.
4x* 3+ 4x* 1 ⇔ 4x(3x+1)
Checking Our Answer
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To check our answer, we can apply the Distributive Property and compare the result with the given expression.
