If $P (x) = 6 x^{3} + 18 x^{2} + 27 x + 30$ has one of the factor $(2 x^{2} + 2 x + 5)$ , then using synthetic division find the other factor of $P (x)$ .

(x + 6)

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(3 x + 6)

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(3 x + 3)

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(2 x + 3)

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Solution

The correct option is B $(3 x + 6)$

SInce $2 x^{2} + 2 x + 5$ is the factor of the polynomial $P (x) = 6 x^{3} + 18 x^{2} + 27 x + 30$ , so, to find the other factor of the given polynomial, we divide $6 x^{3} + 18 x^{2} + 27 x + 30$ by $2 x^{2} + 2 x + 5$ as shown in the above image and we observe that the quotient is $3 x + 6$ and the remainder is $0$ .

Hence, the other factor of $P (x)$ is $3 x + 6$ .

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Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:
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If P(x)=6x3+18x2+27x+30 has one of the factor (2x2+2x+5), then using synthetic division find the other factor of P(x).

If $P (x) = 6 x^{3} + 18 x^{2} + 27 x + 30$ has one of the factor $(2 x^{2} + 2 x + 5)$ , then using synthetic division find the other factor of $P (x)$ .