Determine whether g(x)=x32−x2+2 is a polynomial. If it is, state its degree. If not, say...

Step 1
Given:
${\displaystyle g\left(x\right)=\frac{x^3}{2}-x^2+2}$
Step 2
Convert element to fracnion: ${\displaystyle x^2=\frac{x^{2}2}{2},2=\frac{2\times 2}{2}}$
${\displaystyle =\frac{x^3}{2}-\frac{x^2\times 2}{2}+\frac{2\times 2}{2}}$
Since the denominators are equal, combine the fractions: ${\displaystyle \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm b}{c}}$
${\displaystyle =\frac{x^3-x^2\times 2+2\times 2}{2}}$
Multiply the numbers: ${\displaystyle 2\times 2=4}$
${\displaystyle g\left(x\right)=\frac{x^3-2x^2+4}{2}}$
Hence, it is a polynomial with its degree 3,
Step 3
Now, convert 3 degree polynomial into standard form which is
${\displaystyle a{x}^3+b{x}^3+cx+d}$
Standard form ${\displaystyle \to g\left(x\right)=\frac{x^3}{2}-2x^2+0x+2}$
Leading term ${\displaystyle \to \frac{1}{2}}$
Constant term ${\displaystyle \to 2}$