Find the remainder when $x^4+x^3-2x^2+x+1$ is divided by $x -1$.
$2$
$3$
$4$
$5$
Factorise : $x^{3}-2 x^{2}-x+2$
Expand each of the following, using suitable identities : $\left[\frac{1}{4} a-\frac{1}{2} b+1\right]^{2}$
Factorise : $\frac{25}{4} x^{2}-\frac{y^{2}}{9}$
Factorise $6x^2 + 17x + 5$ by splitting the middle term, and by using the Factor Theorem.
Write the coefficients of $x^2$ in each of the following :
$(i)$ $\frac{\pi}{2} x^{2}+x$ $ (ii)$ $\sqrt{2} x-1$