What is the greatest common factor of the terms in the polynomial 12x⁴ + 27x³ + 6x²?

Solution:

The polynomial 12x⁴ + 27x³ + 6x² can be factorized in the manner below:

3x²(4x² + 9x + 2)

By using splitting of middle term,

3x²(4x² + 8x + x + 2)

3x²(4x(x + 2) + 1(x + 2))

3x²(x + 2)(4x + 1)

Hence the polynomial has three factors which are:

1. 3x²

2. (4x + 1)

3. (x + 2)

The greatest common factor amongst the three factors is 3x² as it has a degree of 2 and a coefficient greater than 1.

What is the greatest common factor of the terms in the polynomial 12x⁴ + 27x³ + 6x²?

Summary:

The greatest common factor amongst the three factors is 3x² as it has a degree of 2 and a coefficient greater than 1.