Verify whether the following are zeroes of the polynomial, indicated against them.
$p(x) = (x + 1) (x -2)$, $x = -\,1, \,2$
If $x=-\,1$ and $x=2$ are zeroes of polynomial $p(x)=(x+1)(x-2),$ then $p(-1)$ and $p (2)$ should be $0$.
Here, $p (-1)=(-1+1)(-1-2)=0(-3)=0,$ and $p (2)$
$=(2+1)(2-2)=3(0)=0$
Therefore, $x=-1$ and $x=2$ are zeroes of the given polynomial.
Find the remainder when $x^{3}+3 x^{2}+3 x+1$ is divided by $x-\frac{1}{2}$
Classify the following as linear, quadratic and cubic polynomials :
$(i)$ $1+x$
$(ii)$ $3 t$
$(iii)$ $r^{2}$
$(iv)$ $7 x^{3}$
Evaluate the following products without multiplying directly : $95 \times 96$
Find the degree of each of the polynomials given below : $2$
Find the degree of the polynomials given : $x^{5}-x^{4}+3$