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Sagot :
Given:
The expression is:
[tex]12x^3+16xy+4x^2[/tex]
To find:
The greatest common factor of the given expression.
Solution:
We have,
[tex]12x^3+16xy+4x^2[/tex]
The terms of the expression are [tex]12x^3, 16xy, 4x^2[/tex]. The factor forms of these terms are:
[tex]12x^3=2\times 2\times 3\times x\times x\times x[/tex]
[tex]16xy=2\times 2\times 2\times 2\times x\times y[/tex]
[tex]4x^2=2\times 2\times x\times x[/tex]
The common factors are 2, 2, x. So, the greatest common factor is:
[tex]G.C.F.=2\times 2\times x[/tex]
[tex]G.C.F.=4x[/tex]
After taking out the G.C.F., the given expression can be written as:
[tex]12x^3+16xy+4x^2=4x(3x^2+4y+x)[/tex]
Therefore, the G.C.F. of the given expression is [tex]4x[/tex].
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