Question

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.

Answer 1

i. False.
A binomial has exactly two terms.

ii. False.
Every polynomial is not a binomial.
e.g., $\begin{array}{cc}\left(a\right)3x^2+4x+5& \text{[polynomial but not a binomial]}\\ \left(b\right)3x^2+5& \text{[polynomial and also a binomial]}\end{array}$

iii. True.
Binomial is a polynomial whose degree is a whole number greater than equal to one. So, it may have degree 5.

iv. False.
Zero of a polynomial can be any real number.

v. False,
A polynomial can have any number of zeroes. It depends upon the degree of the polynomial.

vi. False.
The degree of the sum of any two polynomials of same degree is not always the same.
For example;
Let $f\left(x\right)=x^4+2$ and $g\left(x\right)=-x^4+4x^3+2x$
Sum of two polynomials,
$f\left(x\right)+g\left(x\right)=x^4+2+(-x^4+4x^3+2x)$
$=4x^3+2x+2$ which is not a polynomial of degree 4.