Evaluate $105 \times 106$ without multiplying directly.
$11130$
$10030$
$11120$
$12130$
$105 \times 106=(100+5) \times(100+6)$
$=(100)^{2}+(5+6)(100)+(5 \times 6),$ using Identity $IV$
$=10000+1100+30$
$=11130$
Factorise : $x^{3}-3 x^{2}-9 x-5$
Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases : $p(x)=x^{3}+3 x^{2}+3 x+1$, $g(x)=x+2$.
Factorise : $3 x^{2}-x-4$
Determine which of the following polynomials has $(x + 1)$ a factor : $x^{4}+x^{3}+x^{2}+x+1$.
Find $p(0)$, $p(1)$ and $p(2)$ for of the following polynomials : $p(y)=y^{2}-y+1$
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