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Division Algorithm for a Polynomial

If px= x2-4...

Question

If $p (x) = x^{2} - 4, q (x) = x^{3} - 8, r (x) = (x + 2)$ and $s (x) = (x^{2} + 2 x + 4)$ then choose the correct options -

p (x) . s (x) = q (x) . r (x)

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p (x) . s (x) \neq q (x) . r (x)

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p (x) . q (x) = s (x) . r (x)

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None of these

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Solution

The correct option is A $p (x) . s (x) = q (x) . r (x)$
Here $p (x) = x^{2} - 4 = (x - 2) (x + 2)$
$q (x) = x^{3} - 8 = (x - 2) (x^{2} + 2 x + 4)$
and $r (x) = (x + 2)$
$s (x) = (x^{2} + 2 x + 4)$
Now, $p (x) . s (x) = (x - 2) (x + 2) \times (x^{2} + 2 x + 4)$ ............ (1)
and $q (x) . r (x) = (x - 2) (x^{2} + 2 x + 4) \times (x + 2)$ ........... (2)
Both multiplications comes out to be equal to $x^{4} + 2 x^{3} - 8 x - 16$
From (1) and (2),
$p (x) . s (x) = q (x) . r (x)$

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Similar questions

p (x) = x^{2} + 6 x + 8, q (x) = x^{2} + 5 x + 6, r (x) = x^{2} + 4 x + 3

s (x) = x^{2} + 5 x + 4

p (x)

g (x)

q (x)

r (x)

p (x)

\frac{x - 2}{x^{2} - 4} = \frac{r (x)}{x^{3} + 8}

r (x)

p (x) = x^{2} - 2 x + 1

q (x) = x^{4} - 1

r (x) = x^{3} - 2 x^{2} - 5 x + 6

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)

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