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
$5 x^{2}-7 x+3 \sqrt{x}$
Given expression $5 x^{2}-7 x+3 \sqrt{x}$ is not a polynomial because in term $3 \sqrt{x}=3 x^{\frac{1}{2}}$ the exponent of $x$ is a fractional number.
..........is one of the zeros of the polynomial $x^{3}-3 x^{2}-5 x+15$
$(5 x+3)(5 x-3)=\ldots \ldots . .$
Evaluate the following using suitable identities
$(107)^{2}$
Find the quotient and the remainder when $x^{3}+x^{2}-10 x+8$ is divided by
$x+3$
Factorise
$8 x^{3}-26 x^{2}+13 x+5$