Q.1 Which of the following is a polynomial?
x^2 + 3x + 2
2/x + 3
√x + 4
sin(x) + 1
Explanation - A polynomial has only non-negative integer powers of x. Among the options, x^2 + 3x + 2 satisfies this.
Correct answer is: x^2 + 3x + 2
Q.2 What is the degree of the polynomial 7x^4 + 3x^2 - x + 9?
1
2
3
4
Explanation - The degree of a polynomial is the highest power of x. Here it is 4.
Correct answer is: 4
Q.3 What type of polynomial is 5x + 7?
Monomial
Binomial
Trinomial
Quadrinomial
Explanation - 5x + 7 has two terms, making it a binomial.
Correct answer is: Binomial
Q.4 What is the degree of the constant polynomial 8?
0
1
-1
Undefined
Explanation - Any nonzero constant polynomial has degree 0.
Correct answer is: 0
Q.5 What is the coefficient of x^3 in 6x^3 - 4x + 7?
6
-4
7
3
Explanation - The coefficient of x^3 is the number multiplied by x^3, which is 6.
Correct answer is: 6
Q.6 Which of the following is a monomial?
x^2 + 2x
3x^4
x^2 + y^2
x + 1
Explanation - A monomial has only one term. 3x^4 fits this definition.
Correct answer is: 3x^4
Q.7 If P(x) = x^2 - 5x + 6, what is P(2)?
0
2
4
6
Explanation - Substitute x=2: (2)^2 - 5(2) + 6 = 4 - 10 + 6 = 0.
Correct answer is: 0
Q.8 What is the sum of the roots of x^2 - 3x + 2 = 0?
-3
3
-2
2
Explanation - For ax^2+bx+c=0, sum of roots = -b/a. Here, -(-3)/1 = 3.
Correct answer is: 3
Q.9 Which polynomial has degree 3?
2x^2 + 5
x^3 - 2x + 7
7x + 4
9
Explanation - The highest exponent is 3, so its degree is 3.
Correct answer is: x^3 - 2x + 7
Q.10 What is the remainder when x^2 + 3x + 2 is divided by (x+1)?
0
2
-1
3
Explanation - By remainder theorem, substitute x = -1: (-1)^2+3(-1)+2 = 1-3+2=0.
Correct answer is: 0
Q.11 If f(x) = x^2 + 4x + 3, what is f(-3)?
0
3
-2
-6
Explanation - Substitute x=-3: (-3)^2 + 4(-3) + 3 = 9 -12 +3 = 0.
Correct answer is: 0
Q.12 Which of these polynomials is a trinomial?
x^2
x^2 + 3x
x^2 + 3x + 1
x^2 + 3
Explanation - A trinomial has three terms, like x^2 + 3x + 1.
Correct answer is: x^2 + 3x + 1
Q.13 What is the degree of 7x^5 + 4x^3 + 2?
2
3
4
5
Explanation - The highest power is 5, so degree is 5.
Correct answer is: 5
Q.14 What is the leading coefficient of 9x^4 - 7x^2 + 5?
9
-7
5
4
Explanation - The leading coefficient is the coefficient of the highest degree term, which is 9.
Correct answer is: 9
Q.15 If a polynomial has degree 0, what kind of polynomial is it?
Zero polynomial
Constant polynomial
Linear polynomial
Quadratic polynomial
Explanation - Degree 0 polynomials are constant values (non-zero).
Correct answer is: Constant polynomial
Q.16 What is the product of (x+2)(x+3)?
x^2+6
x^2+5x+6
x^2+2x+3
x^2+5x+9
Explanation - Expanding: (x+2)(x+3) = x^2+3x+2x+6 = x^2+5x+6.
Correct answer is: x^2+5x+6
Q.17 Which of the following is NOT a polynomial?
2x^2+3x+1
4/x + 5
x^4+7
3x^3-2x+9
Explanation - Polynomials cannot have negative powers of x, but 4/x means x^-1.
Correct answer is: 4/x + 5
Q.18 If (x-2) is a factor of x^2 - 4, what is the other factor?
x+2
x-4
x+4
x-1
Explanation - x^2-4 is a difference of squares = (x-2)(x+2).
Correct answer is: x+2
Q.19 What is the degree of the zero polynomial?
0
-1
Undefined
1
Explanation - Zero polynomial has no well-defined degree.
Correct answer is: Undefined
Q.20 If P(x) = x^2 + x + 1, what is P(0)?
0
1
2
-1
Explanation - Substituting x=0 gives 0+0+1=1.
Correct answer is: 1
Q.21 The polynomial x^2 + 6x + 9 can be factored as:
(x+9)(x+1)
(x+3)(x+3)
(x+2)(x+4)
(x+6)(x+1)
Explanation - x^2+6x+9 is a perfect square trinomial = (x+3)^2.
Correct answer is: (x+3)(x+3)
Q.22 If (x+1) is a factor of P(x), what is P(-1)?
0
1
-1
Undefined
Explanation - By factor theorem, if (x+1) is a factor, substituting x=-1 gives remainder 0.
Correct answer is: 0
Q.23 What is the degree of 2x^2y^3 + x^4?
4
5
6
7
Explanation - Degree of a term is sum of exponents. First term: 2+3=5, second term=4, so degree is 5.
Correct answer is: 5
Q.24 What is the value of (x+2)(x-2)?
x^2+4
x^2-4
x^2+2
x^2-2
Explanation - By difference of squares: (x+2)(x-2)=x^2-4.
Correct answer is: x^2-4
Q.25 The polynomial 3x^3+5x^2-2x+1 is of degree:
1
2
3
4
Explanation - Highest exponent is 3, so degree is 3.
Correct answer is: 3