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evablogger [386]
3 years ago
7

50 points!!! Factor completely 3n^4+21n^3+27n^2 Please show work!!

Mathematics
1 answer:
Elden [556K]3 years ago
5 0

Answer:

3n^2(n^2+7n+9)

Step-by-step explanation:

Find the common factor. In this case, it is 3n^2. Take out the common factor of the integers.

So, therefore it is

3n^2(n^2+7n+9)

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~~~~~~x^2 +3x +21 = 0\\\\\implies x^2 +3x = -21\\\\\implies x^2 + 2\cdot  \dfrac 32 \cdot x + \left( \dfrac 32 \right)^2 = -21 + \left( \dfrac 32 \right)^2\\\\\implies \left(x + \dfrac 32 \right)^2 = -21+\dfrac 94\\\\\implies \left(x + \dfrac 32 \right)^2 = -\dfrac{75}4\\\\\implies x+ \dfrac 32 = \pm\sqrt{-\dfrac{75}4 \right)\\\\\implies x + \dfrac 32 = \pm i \dfrac{5\sqrt 3}{2}\\\\\implies x = -\dfrac 32 \pm i \dfrac {5\sqrt 3}2\\\\\implies x = \dfrac 12 \left( -3 \pm  i5\sqrt 3\right)

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