I need to fator this polynomail completly: 4g^2(g-3)+(g-3)

Question

I need to fator this polnomail completly 4g^2(g-3)+(g-3)

Answer 1

To completely factor the polynomial, 4g²(g - 3) + (g-3), we must begin by pulling out the common factor
(g - 3) from both terms of this polynomial, which gives us (g - 3)(4g² + 1). If the other factor (4g² + 1) was instead (4g²  -1 ) then we could apply the factoring pattern for the difference of two perfect squares (a² - b²), which is (a + b)(a - b) where in our case we would substitute 2g for a and 1 for b giving us the factors of (2g + 1)(2g - 1).  However, since our other factor is the addition of two perfect squares
(4g² + 1), our final answer is (g - 3)(4g² + 1).

Answer 2

If you are learning imaginary numbers as well you could go one step further:

4g^2(g-3)+(g-3) = (g-3)(4g^2+1) = (g-3)(2g+i)(2g-i)

Answer 3

The correct answer should be

4g²(g-3)+(g-3) = (g-3)(4g² + 1)