Question

Why is \[\frac{x^{2}+1}{x^{2}-5x+6}\] not a proper rational function?

Options

• Because \[\deg(x^{2}+1)=\deg(x^{2}-5x+6)\].

• Because \[x^{2}+1=0\].

• Because \[\deg(x^{2}+1)<\deg(x^{2}-5x+6)\].

• Because the denominator has no factors.

Answer 1

Both numerator and denominator have degree \[2\]. Since the numerator degree is greater than or equal to the denominator degree, the rational function is improper.