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

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3 Answers

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).

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)


To clarify:

"i" stands for imaginary number:

(2g+i) (2g-i) = 4g2 - i2 = 4g2-(-1) = 4g2+1