Classify the following polynomial as linear,quadratic,or cubic: $4x^{2} - 49$.

Which one of the following is a polynomial?

State whether the following statement is true or false:
$x^{2}-8x+12 = (x-6)(x-2)$

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

Which of the following expressions is a polynomial? State the reason. If an expression is a polynomial,state whether it is a polynomial in one variable or not: $x^{2}+y^{2}+z^{2}+2xy+2yz+2zx$

If both $x-2$ and $x-\frac{1}{2}$ are factors of $p x^{2}+5 x+r,$ show that $p=r$.