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:

$12x^3=2\times 2\times 3\times x\times x\times x$

$16xy=2\times 2\times 2\times 2\times x\times y$

$4x^2=2\times 2\times x\times x$

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

$G.C.F.=2\times 2\times x$

$G.C.F.=4x$

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 $4x$.