[CLASS 9] Mathematics MCQs on Polynomials Basics and Answers

Mathematics Multiple Choice Questions on “Polynomials Basics”.

1. What is the coefficient of x³ in a polynomial 6x⁴ + 3x² + 8x + 5?
a) 6
b) 3
c) 8
d) 0

Answer: d
Clarification: Coefficient is the number which is multiplied with respective variable.
In the given polynomial 6x⁴ + 3x² + 8x + 5, there is not an expression containing x³. So we can write 6x⁴+ 3x²+8x+5 as 6x⁴ + 0x³ + 3x² + 8x + 5. We can see that 0 is multiplied with expression x³, so coefficient of x³ is 0.

2. (frac{1}{sqrt[2]{x}}) is a polynomial.
a) True
b) False

Answer: b
Clarification: 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 4x⁷+9x⁵+5x²+11?
a) 7
b) 4
c) 5
d) 2

Answer: a
Clarification: Degree of a polynomial is the highest power of variable in a polynomial.
The term with the highest power of x is 4x⁷ and exponent of x in that term is 7, so the degree of polynomial of 4x⁷+ 9x⁵+5x²+11 is 7.

4. What is the degree of a polynomial 7?
a) 7
b) 1
c) 0
d) 2

Answer: c
Clarification: 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 7x⁰.
Hence degree of 7 is zero.

5. What is the degree of 0?
a) Not defined
b) 1
c) 2
d) 0

Answer: a
Clarification: 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

Answer: d
Clarification: A polynomial of degree 2 is called quadratic polynomial.
Quadratic polynomials are of the form ax²+bx+c and it can contain at most three terms namely ax², 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.