Question

The degree of the sum of two polynomials each of degree 5 is always 5.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

Because the sum of any two polynomials of same degree is not always same degree.

e.g., Let f(x) = x⁴ + 2 and g(x) = –x⁴ + 4x³ + 2x

∴ Sum of two polynomials, f(x) + g(x) = x⁴ + 2 + (–x⁴ + 4x³ + 2x) = 4x³ + 2x + 2 which is not a polynomial of degree 4.