# Mathematics Questions and Answers – Polynomials Basics

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses 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

Explanation: 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

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

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

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 7x0.
Hence degree of 7 is zero.

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

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

Explanation: 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.

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