State whether the following statement is True or False.
Polynomial of different degrees cannot be added.

True

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False

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Solution

The correct option is B False
Degree of polynomials:
If a polynomial is in one variable, the highest power of the polynomial is called the degree of the polynomial.
When the polynomial is in two variables, the sum of the powers of the variable in each term is taken up, and the highest sum so obtained, is called the degree of the polynomial.
Let's take two polynomials $x^{2} + 5 x + 9$ and $3 x$ .
The degree of $x^{2} + 5 x + 9$ is 2 and the degree of $3 x$ is 1.
On adding the 2 polynomials, we get:
$x^{2} + 5 x + 9 + 3 x = x^{2} + 8 x + 9$
Hence, the polynomials of different degrees can be added.
Hence, the given statement is false.

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