Write whether statement are True or False. Justify your answer. degree of sum of two polynomials eac

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2. Polynomials

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Write whether the statement are True or False. Justify your answer.

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

Option A

Option B

Option C

Option D

Solution

The given statement is false. For example, consider the two polynomial $-x^{5}+3 x^{2}+4$ and $x^{5}+x^{4}+2 x^{3}+3 .$

The degree of each of these polynomial is $5 .$

Their sum is $x^{4}+2 x^{3}+3 x^{2}+7 .$

The degree of this polynomial is not $5$

Standard 9

Mathematics

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