Find common factor of $P (x) = 15 x^{2} + 19 x + 6$ and $Q (x) = 3 x^{2} + 14 x + 8$ using synthetic division.

(3 x + 2)

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(5 x + 3)

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(x + 4)

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(2 x + 1)

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Solution

The correct option is A $(3 x + 2)$
$P (x) = {15 x}^{2} + 19 x + 6 P (x) = {15 x}^{2} + 10 x + 9 x + 6 P (x) = 5 x (3 x + 2) + 3 (3 x + 2) P (x) = (5 x + 3) (3 x + 2) Q (x) = {3 x}^{2} + 14 x + 8 Q (x) = {3 x}^{2} + 12 x + 2 x + 8 Q (x) = 3 x (x + 4) + 2 (x + 4) Q (x) = (3 x + 2) (x + 4)$
So $(3 x + 2)$ is the common factor
Option $A$ is correct.

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