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Factorisation of Quadratic Polynomials - Factor Theorem

If x+3 and ...

Question

If $(x + 3)$ and $(x^{2} + 5 x + 7)$ are the factors of the polynomial $P (x) = a x^{3} + b x^{2} + c x + d$ , then find $c$ .

A

1

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B

8

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C

21

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D

22

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Solution

The correct option is C $21$
As $(x + 3)$ and $(x^{2} + 5 x + 7)$ are the factors of $P (x)$
$\Rightarrow P (x) = (x + 3) {(x}^{2} + 5 x + 7) \Rightarrow P (x) = x^{3} + 5 x^{2} + 7 x + 3 x^{2} + 15 x + 21 \Rightarrow P (x) = x^{3} + 8 x^{2} + 22 x + 21$
Comparing with the given polynomial $P (x)$
We get $c = 21$
So option $C$ is correct

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