Say true or false:
The degree of the sum of two polynomials each of degree $5$ is always $5$ .

True

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False

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Solution

The correct option is B False
It is not necessary that the degree of the sum of two polynomials each of degree $5$ is always $5$ .
Let $p (x) = - x^{5} + x^{2} + 2$ and $q (x) = x^{5} + x^{3} + 4$
$p (x)$ and $q (x)$ each are of degree $5$ .
But $p (x) + q (x)$ $= - x^{5} + x^{2} + 2 + x^{5} + x^{3} + 4 = x^{3} + x^{2} + 6$ which is not of degree $5$ .

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Similar questions

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

Question 2
Write whether the following statements are true or false. Justify your answer.

i. A Binomial can have atmost two terms.

ii. Every polynomial is a Binomial.

iii. A binomial may have degree 5.

iv. Zero of a polynomial is always 0.

v. A polynomial cannot have more than one zero.

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

Q. Say true or false:

The zero of

x - 5

5

Q. Say true or false:
The value of

sin θ + cos θ

is always greater than

1

Q. State whether true or false:
The positive degree of comparison is used to compare more than two people or things.

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Say true or false:The degree of the sum of two polynomials each of degree 5 is always 5.

The correct option is B FalseIt is not necessary that the degree of the sum of two polynomials each of degree 5 is always 5.Let p(x)=−x5+x2+2 and q(x)=x5+x3+4p(x) and q(x) each are of degree 5.But p(x)+q(x) =−x5+x2+2+x5+x3+4=x3+x2+6 which is not of degree 5.

Say true or false:
The degree of the sum of two polynomials each of degree $5$ is always $5$ .