Which of the following expressions are polynomials in one variable and which are not $?$ State reason for your answer. If the given expression is a polynomial, state whether it is a polynomial in one variable or not
$x^{2}-8 x+15$
Given expression $x^{2}-8 x+15$ is a polynomial because the exponent of variable $x$ in each of its terms is an integer, viz., $2 , 1$ and $0$ respectively. The given polynomial is a polynomial, in one variable $x$.
Factorise the following:
$8 p^{3}+\frac{12}{5} p^{2}+\frac{6}{25} p+\frac{1}{125}$
Factorise each of the following
$8 x^{3}+343 y^{3}+84 x^{2} y+294 x y^{2}$
For polynomial $p(x)=x^{3}-3 x^{2}+8 x+12$, $p(-1)=\ldots \ldots \ldots$
Multiply $x^{2}+4 y^{2}+z^{2}+2 x y+x z-2 y z$ by $(-z+x-2 y)$
Is $(x-1)$ is a factor of $3 x^{2}+7 x-10 ?$