# What is a second degree polynomial?

Oct 28, 2015

A second degree polynomial is a polynomial $P \left(x\right) = a {x}^{2} + b x + c$, where $a \ne 0$

#### Explanation:

A degree of a polynomial is the highest power of the unknown with nonzero coefficient, so the second degree polynomial is any function in form of:

$P \left(x\right) = a {x}^{2} + b x + c$ for any a in RR-{0};b,c in RR

Examples

${P}_{1} \left(x\right) = 2 {x}^{2} - 3 x + 7$ - this is a second degree polynomial

${P}_{2} \left(x\right) = 3 x + 7$ - this is not a second degree polynomial (there is no ${x}^{2}$)

${P}_{3} \left(x\right) = {x}^{2} - 1$ - this is a second degree polynomial ($b$ or $c$ can be zero)

${P}_{4} \left(x\right) = {x}^{2} - \frac{1}{x}$ - this is not a polynomial ($x$ is not allowed in the denominator)