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Factor Theorem

If x3 - 18x -...

Question

If $x^{3} - 18 x - 35 = (x - 5) . p (x)$ .
Find polynimial $p (x)$ .

$x^{2} + 7 x + 5$

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$x^{2} + 3 x + 2$

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$x^{2} + 2 x + 3$

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$x^{2} + 5 x + 7$

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Solution

The correct option is D
$x^{2} + 5 x + 7$

Using long division method, we have $\begin{matrix} x^{2} + 5 x + 7 x - 3 & x^{3} - 18 x - 35_x^{3}_+ 5 x^{2} 5 x^{2} - 18 x_{-} 5 x^{2}_{+} - 25 x 7 x - 35 7 x - 35 0 \end{matrix}$

Quotient is $x^{2} + 5 x + 7$ .
$\Rightarrow x^{3} - 18 x - 35 = (x - 5) . (x^{2} + 5 x + 7)$ .

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Similar questions

Now in each of the following, find the quotient and remainder on dividing p(x) by q(x) and write then in the form p(x) = u(x) q(x) + v(x).

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

x - \frac{1}{x} + 2

\frac{1}{x} + 5

\sqrt{x} + 3

If (x+5) is a factor of p $(x) = x^{3} - 20 x + 5$ k then k=?
(a) -5 (b) 5 (c) 3 (d)-3

If (x - 5) is a factor of the cubic equation $x^{3} - 18 x - 35 = 0$ . Find the quotient.

x^{3} - 18 x = 35

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