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Division of a Polynomial by a Polynomial

The L.C.M of ...

Question

The L.C.M of two polynomials p(x) and q(x) is $(x + 3) (x - 2)^{2} (x - 6)$ and their H.C.F is (x-2). If $p (x) = (x + 3) (x - 2)^{2},$ then $q (x) = . . . . . . . . . .$

(x + 3) (x - 2)

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x^{2} - 3 x - 18

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x^{2} - 8 x + 12

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x^{2} - 4 x + 4

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Solution

The correct option is C $x^{2} - 8 x + 12$
(C) $\frac{L C M \times H C F}{p (x)} = q (x)$
$\frac{(x + 3) (x - 2)^{2} (x - 6) \times (x - 2)}{(x + 3) (x - 2)^{2}} = q (x)$

$\Rightarrow x^{2} - 8 x + 12 = q (x)$

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Similar questions

p (x)

q (x)

(x + 3) (x - 2)^{2} (x - 6)

(x - 2)

p (x) = (x + 3) (x - 2)^{2}

q (x) =

q (x)

(x + 1)^{2}

(x + 2)^{2}

p (x)

x^{2} + 3 x + 2

=

m (x) = x^{2} - 3 x + 2

Now for each pair of polynomials p(x) and q(x) given below, find p(x) + q(x) and p(x) − q(x). Also compute p(1) + q(1) and p(1) − q(1) for each.

(i)

(ii)

(iii)

(iv)

(v)

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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