Use suitable identities to find the products : $(3-2 x)(3+2 x)$
$(3-2 x)(3+2 x)$
Using the identity $(a+b)(a-b)=a^{2}-b^{2},$ we have :
$(3-2 x)(3+2 x)=(3)^{2}-(2 x)^{2}=9-4 x^{2}$
Check whether $7+3 x$ is a factor of $3 x^{3}+7 x$.
Factorise $4 x^{2}+y^{2}+z^{2}-4 x y-2 y z+4 x z$.
Find the value of $k$, if $x -1$ is a factor of $p(x)$ in this case : $p(x)=k x^{2}-\sqrt{2} x+1$
Check whether the polynomial $q(t)=4 t^{3}+4 t^{2}-t-1$ is a multiple of $2 t+1$.
Use the Factor Theorem to determine whether $g(x)$ is a factor of $p(x)$ in each of the following cases : $p(x)=2 x^{3}+x^{2}-2 x-1$, $g(x)=x+1$.
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