Question

Greatest common factor of 4ax^2+4ax+4a

Answer 1

Answer:
The greatest common factor is 4

Explanation: all terms in the equation can be divided by four

Answer 2

Simplifying

4AX2 + 4AX + 4A = 0

Reorder the terms:

4A + 4AX + 4AX2 = 0

Solving

4A + 4AX + 4AX2 = 0

Solving for variable 'A'.

Move all terms containing A to the left, all other terms to the right.

Factor out the Greatest Common Factor (GCF), '4A'.

4A(1 + X + X2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor 'A' equal to zero and attempt to solve:

Simplifying

A = 0

Solving

A = 0

Move all terms containing A to the left, all other terms to the right.

Simplifying

A = 0

Subproblem 2

Set the factor '(1 + X + X2)' equal to zero and attempt to solve:

Simplifying

1 + X + X2 = 0

Solving

1 + X + X2 = 0

Move all terms containing A to the left, all other terms to the right.

Add '-1' to each side of the equation.

1 + X + -1 + X2 = 0 + -1

Reorder the terms:

1 + -1 + X + X2 = 0 + -1

Combine like terms: 1 + -1 = 0

0 + X + X2 = 0 + -1

X + X2 = 0 + -1

Combine like terms: 0 + -1 = -1

X + X2 = -1

Add '-1X' to each side of the equation.

X + -1X + X2 = -1 + -1X

Combine like terms: X + -1X = 0

0 + X2 = -1 + -1X

X2 = -1 + -1X

Add '-1X2' to each side of the equation.

X2 + -1X2 = -1 + -1X + -1X2

Combine like terms: X2 + -1X2 = 0

0 = -1 + -1X + -1X2

Simplifying

0 = -1 + -1X + -1X2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Solution

A = {0}