The degree of the sum of two polynomials each of degree 5 is always 5. Is the given statement true or false? Justify your answer

Solution:

The degree of the sum of two polynomials of the same degree is not always the same.

Example

Consider f (x) = x⁴ + 2

g(x) = -x⁴ + 4x³ + 2x

Sum = f(x) + g(x)

= x⁴ + 2 - x⁴ + 4x³ + 2x

So we get

= 4x³ + 2x + 2 is not a polynomial of degree 4

Therefore, the statement is false.

✦ Try This: 1/ (x + 8). Is the given statement true or false? Justify your answer

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2

NCERT Exemplar Class 9 Maths Exercise 2.2 Problem 2(vi)

The degree of the sum of two polynomials each of degree 5 is always 5. Is the given statement true or false? Justify your answer

Summary:

The degree of a polynomial is the highest exponential power in the polynomial equation. The statement “The degree of the sum of two polynomials each of degree 5 is always 5” is false

☛ Related Questions:

• Check whether p(x) is a multiple of g(x) or not, where p(x) = x³ - x + 1, g(x) = 2 - 3x
• Check whether g(x) is a factor of p(x) or not, where p(x) = 8x³ - 6x² - 4x + 3, g(x) = x/3 - 1/4
• Find the value of a, if x - a is a factor of x³ - ax² + 2x + a - 1