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

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

# 3 Answers

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).

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)

# Comments

To clarify:

"i" stands for imaginary number:

(2g+i) (2g-i) = 4g^{2} - i^{2} = 4g^{2}-(-1) = 4g^{2}+1

The correct answer should be

4g^{2}(g-3)+(g-3) = (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)]

Comment