Question

Greatest common factor of 12x^3+16xy+4x^2

Answer 1

Given:

The expression is:

`12x^3+16xy+4x^2`

To find:

The greatest common factor of the given expression.

Solution:

We have,

`12x^3+16xy+4x^2`

The terms of the expression are
`12x^3, 16xy, 4x^2`. The factor forms of these terms are:

`12x^3=2* 2* 3* x* x* x`

`16xy=2* 2* 2* 2* x* y`

`4x^2=2* 2* x* x`

The common factors are 2, 2, x. So, the greatest common factor is:

`G.C.F.=2* 2* x`

`G.C.F.=4x`

After taking out the G.C.F., the given expression can be written as:

`12x^3+16xy+4x^2=4x(3x^2+4y+x)`

Therefore, the G.C.F. of the given expression is
`4x`.