Verify whether the following are True or False:
$\frac{-4}{5}$ is a zero of $4-5 y$
A zero of a polynomial $p ( x )$ is a number $c$ such that $p ( c )=0$
Let $p(y)=4-5 y$
$\therefore \quad p\left(-\frac{4}{5}\right)=4-5\left(\frac{-4}{5}\right)=4+4=8 \neq 0.$
Hence, $-\frac{4}{5}$ is not a zero of $4-5 y.$
Find the following products:
$\left(x^{2}-1\right)\left(x^{4}+x^{2}+1\right)$
Simplify $(2 x-5 y)^{3}-(2 x+5 y)^{3}$
State whether each of the following statements is true or false
In polynomial $5 x^{3}-3 x^{2}+11 x-14,$ the coefficient of $x^{3}$ is $3.$
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
$x-1$
Factorise
$8 x^{3}-26 x^{2}+13 x+5$