This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Polynomials Basics”.

1. What is the coefficient of x^{3} in a polynomial 6x^{4} + 3x^{2} + 8x + 5?

a) 6

b) 3

c) 8

d) 0

View Answer

Explanation: Coefficient is the number which is multiplied with respective variable.

In the given polynomial 6x

^{4}+ 3x

^{2}+ 8x + 5, there is not an expression containing x

^{3}. So we can write 6x

^{4}+ 3x

^{2}+8x+5 as 6x

^{4}+ 0x

^{3}+ 3x

^{2}+ 8x + 5. We can see that 0 is multiplied with expression x

^{3}, so coefficient of x

^{3}is 0.

2. \(\frac{1}{\sqrt[2]{x}}\) is a polynomial.

a) True

b) False

View Answer

Explanation: For an expression to be a polynomial, exponent of variable has to be whole number.

\(\frac{1}{\sqrt[2]{x}}\) can be written as x

^{-1/2}. We can see that exponent of x is -1/2 which is not whole number (W = {0, 1, 2, 3…}). Hence, \(\frac{1}{\sqrt[2]{x}}\) is not a polynomial.

3. What is the degree of a polynomial of 4x^{7}+9x^{5}+5x^{2}+11?

a) 7

b) 4

c) 5

d) 2

View Answer

Explanation: Degree of a polynomial is the highest power of variable in a polynomial.

The term with the highest power of x is 4x

^{7}and exponent of x in that term is 7, so the degree of polynomial of 4x

^{7}+ 9x

^{5}+5x

^{2}+11 is 7.

4. What is the degree of a polynomial 7?

a) 7

b) 1

c) 0

d) 2

View Answer

Explanation:

**Degree of a non-zero constant polynomial is zero**.

We can see that given polynomial 7 contain only one term and that is constant. 7 can also be written as 7x

^{0}.

Hence degree of 7 is zero.

5. What is the degree of 0?

a) Not defined

b) 1

c) 2

d) 0

View Answer

Explanation:

**Degree of the zero polynomial is not defined**.

Zero polynomial is denoted by 0, and degree for that is not defined.

6. A quadratic polynomial can have at most __________ terms.

a) 1

b) 4

c) 2

d) 3

View Answer

Explanation:

**A polynomial of degree 2 is called quadratic polynomial**.

Quadratic polynomials are of the form ax

^{2}+bx+c and it can contain at most three terms namely ax

^{2}, bx and c. Thus, we can say that a quadratic polynomial can have at most three terms.

Similarly,

**a polynomial of degree 1 is called linear polynomial and a polynomial of degree 3 is called cubic polynomial**.

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