Algebra and Trigonometry 10th Edition

False. Normally it is true, but if the sum of the leading coefficients is equal to $0$, then the sum of the two second-degree polynomials is not a second-degree polynomial.
$(ax^2+bx^2+c)+(Ax^2+Bx+C)=(a+A)x^2+(b+B)x+(c+C)$ It is a second-degree polynomial unless $a+A=0$