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Factorisation of Quadratic Polynomials - Factor Theorem

If a polynomi...

Question

If a polynomial $p (x)$ is divided by $x - 2$ , the quotient is $2 x$ and remainder is $4$ . then $p (x)$ =_______?

(x - 2) 4 + 2 x

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2 x \times 4 + (x - 2)

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(x - 4) 2 x + 2

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(x - 2) 2 x + 4

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Solution

The correct option is D $(x - 2) 2 x + 4$
Divisor $= x - 2$
quotient $= 2 x$
Remainder $= 4$
$P (x) = ?$
Divident $=$ divisor $\times$ quotient $+$ Remainder
$P (x) = [(x - 2) (2 x)] + 4$
$= 2 x^{2} - 4 x + 4$
$= (x - 2) 2 x + 4$

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