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$(2 x-3)(2 x+5)$

With the help of the remainder theorem, find the remainder when the polynomial $x^{3}+x^{2}-26 x+24$ is divided by each of the following divisors

$x+1$

If $a, b, c$ are all non-zero and $a+b+c=0,$ prove that $\frac{a^{2}}{b c}+\frac{b^{2}}{c a}+\frac{c^{2}}{a b}=3$

Evaluate the following products without multiplying directly

$103 \times 105$

From the following polynomials find out which of them has $(x-1)$ as a factor

$x^{3}+4 x^{2}+x-6$