If x3−18x−35=(x−5).p(x). Find polynimial p(x).
x2+2x+3
x2+3x+2
x2+7x+5
x2+5x+7
Using long division method, we have x2+5x+7x−3x3−18x−35 _x3_+5x2 5x2−18x −5x2 +−25x 7x−35 7x−35 0
Quotient is x2+5x+7 . ⇒x3−18x−35=(x−5).(x2+5x+7).
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)