Factors of 13c2−2c−9 are

13c2−2c−9=13c2−6c−27=13c2−9c+3c−27=13[c(c−9)+3(c−9)]=13(c+3)(c−9)=13c−3(c+3)

Factors of 13c2−2c−9 are

13c2−2c−9=13c2−6c−27=13c2−9c+3c−27=13[c(c−9)+3(c−9)]=13(c+3)(c−9)=13c−3(c+3)

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Factors of $\frac{1}{3} c^{2} - 2 c - 9$ are

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$(\frac{1}{3} c + 3) (c + 3)$

$(\frac{1}{3} c - 3) (c + 3)$

$(\frac{1}{3} c - 3) (c - 3)$

$(c - \frac{1}{3}) (3 c + 1)$

answer is C.

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Detailed Solution

$\frac{1}{3} c^{2} - 2 c - 9$

$\begin{array}{l} = \frac{1}{3} (c^{2} - 6 c - 27) = \frac{1}{3} (c^{2} - 9 c + 3 c - 27) \\ = \frac{1}{3} [c (c - 9) + 3 (c - 9)] = \frac{1}{3} (c + 3) (c - 9) \\ = (\frac{1}{3} c - 3) (c + 3) \end{array}$

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