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Question
The degree of the sum of two polynomials each of degree 5 is always 5.
Options
True
False
Solution
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.
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