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$x+3$ is a factor of $69+11 x-x^{2}+x^{3}$.

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

$x-6$

Write whether the statement are True or False. Justify your answer.

Zero of a polynomial is always $0.$

Find $p(1), p(2)$ and $p(4)$ for each of the following polynomials

$p(y)=y^{2}-5 y+4$

On dividing $p(x)=2 x^{3}-3 x^{2}+a x-3 a+9$ by $(x+1),$ if the remainder is $16,$ then find the value of $a$. Then, find the remainder on dividing $p(x)$ by $x+2$