Question

02 . The polynomial a³- 3a² + a + 2 is divided by a polynomial g(a). The quotient andremainder obtained are (a -2) and (-2a + 4) respectively. Find g(a).
(A) a² + a + 1
(B) a²- a + 1
(C) a²- a - 1
(D) a² + a - 1​

Answer 1

Solution:-

Given:-

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

$quotient = q(x) = a - 2$

$remainder = r(x) = - 2a + 4$

Now,by using division algorithm:-

$p(x) = q(x).g(x) + r(x)$

We can rearrange it as follows:-

$g(x) = \frac{p(x) - r(x)}{q(x)}$

By putting the given values:

$= > g(x) = \frac{ {a}^{3} - 3 {a}^{2} + a + 2 + 2a - 4}{a - 2}$

$= > g(x) = \frac{ {a}^{3} - 3 {a}^{2} + 3a - 2 }{a - 2}$

By dividing,we get:-

$= > g(x) = {a}^{2} - a + 1$

Hence, option B is correct.