A. Is the sum of two polynomials always a polynomial? Explain

b. Is the difference of two polynomials always a polynomial? Explain

Answer: The answers for both (a) and (b) is YES.

Step-by-step explanation: A polynomial is an algebraic expression containing two or more algebraic terms, i. e., the sum of several terms that contain different powers of the same variable or variables with real coefficients.

For example, p (x) = 4x²+x+2 is a polynomial in variable 'x'.

(a) Yes, the sum of two polynomials is again a polynomial. For example,

if p (x) = ax² + bx + c and q (x) = dx² + ex + f, where, a, b, c, d, e and f are real numbers, then their sum will be

p (x) + q (x) = (a+d) x² + (b+e) x + (c+f), which is again a polynomial in 'x' with real coefficients.

(b) Yes, the difference of two polynomials is again a polynomial. For example,

p (x) - q (x) = (a-d) x² + (b-e) x + (c-f), which is again a polynomial in 'x' with real coefficients.

Thus, the answer is YES.