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

To completely factor the polynomial, 4g^{2}(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)(4g^{2} + 1). If the other factor (4g^{2} + 1) was instead (4g^{2} -1 ) then we could apply the factoring pattern for the difference of two perfect squares (a^{2} - b^{2}), 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

(4g^{2} + 1), our final answer is (g - 3)(4g^{2} + 1).

## Comments

Need to clarify since this could be understood several ways

is it

(4g^2)(g-3)+(g-3)

or

[4g^2(g-3)]+(g-3)

or

4g^[2(g-3)+(g-3)]