Polynomials - MCQs

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Maths — Polynomials

50 Questions Class 10 MCQs
1
A polynomial of degree 0 is called a ____
2
The degree of the polynomial \(5x^4 - 3x^2 + 2x - 7\) is ____
3
The degree of the zero polynomial is ____
4
The coefficient of \(x^2\) in \(5x^3 + 7x^2 - 4x + 9\) is ____
5
A linear polynomial has degree ____
6
Which of the following is a quadratic polynomial?
7
The zero of the polynomial \(p(x) = x - 3\) is ____
8
The zero of \(p(x) = 2x + 5\) is ____
9
The number of zeros of a cubic polynomial is ____
10
The zeros of the polynomial \(p(x) = x^2 - 1\) are ____
11
The value of \(p(x) = x^2 - 2x + 3\) at \(x = 2\) is ____
12
When \(p(x)\) is divided by \(x - a\), the remainder is \(p(a)\). This is called ____
13
If \(p(x) = x^2 + 2x + 1\), zeros are ____
14
The sum of zeros of \(x^2 - 5x + 6\) is ____
15
The product of zeros of \(2x^2 + 5x + 3\) is ____
16
If zeros of \(x^2 - 7x + 10\) are \(\alpha\) and \(\beta\), then \(\alpha + \beta =\) ____
17
The polynomial whose zeros are 2 and 3 is ____
18
If zeros are equal, the discriminant \(b^2 - 4ac\) is ____
19
If \(x = 1\) is a zero of \(x^3 - 3x^2 + x + 1\), then the remainder is ____
20
Factorise \(x^2 - 16\).
21
Polynomial having zeros at -2 and 5 is ____
22
Zeros of \(x^2 + 9\) are ____
23
If one zero of \(2x^2 + 3x - 5\) is 1, the other is ____
24
A cubic polynomial has maximum how many zeros?
25
The remainder when \(x^3 - 2x^2 + 4x - 8\) is divided by \(x - 2\) is ____
26
\(p(x)\) is divisible by \(x - 3\) if ____
27
Zeros of \(x^2 - 3x + 2\) are ____
28
For \(p(x) = x^2 + 4x + 3\), sum of zeros = ____
29
For \(p(x) = x^2 - 2x + 1\), zeros are ____
30
If a polynomial is divisible by both \(x - 1\) and \(x + 2\), then \(p(1)\) and \(p(-2)\) are ____
31
For \(x^2 - 2kx + (k^2 - 1) = 0\), equal roots are possible when ____
32
If \(p(x)\) divided by \(x - 1\) gives remainder 5, find \(p(1)\).
33
If zeros of \(x^2 + 7x + 10\) are a, ß, find aß.
34
The number of terms in \(3x^2 + 2x - 7\) is ____
35
The degree of \(5y^3 - 4y^5 + 3y\) is ____
36
If \(p(x) = x^2 - 4\), then zeros are ____
37
For \(p(x) = ax^2 + bx + c\), if one zero = 0, then \(c\) = ____
38
The graph of a quadratic polynomial is a ____
39
The graph of a linear polynomial is a ____
40
If the graph of polynomial \(p(x)\) touches x-axis at one point, it has ____
41
The product of zeros of \(3x^2 - 2x - 1\) is ____
42
If zeros of \(x^2 - kx + 9\) are equal, then \(k \)= ____
43
If \(x = 2\) is zero of \(x^3 - 2x^2 + 4x - 8\), quotient polynomial is ____
44
For \(p(x) = 3x^2 - 5x + 2\), sum of zeros = ____
45
A polynomial of degree 3 is called ____
46
If zeros are 1 and -3, the polynomial is ____
47
\(x^2 - 4x + 3 = 0\) has how many zeros?
48
Zeros of \(x^3 - 6x^2 + 11x - 6\) are ____
49
For quadratic \(ax^2 + bx + c\), the relationship between coefficients and zeros is ____
50
If zeros of polynomial are 4 and 5, find polynomial with leading coefficient 2.
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Frequently Asked Questions

A polynomial is an algebraic expression that combines variables and numbers, using only non-negative whole number exponents.

Polynomials are classified by their highest exponent: linear (power one), quadratic (power two), cubic (power three), and higher-degree polynomials.

The degree of a polynomial is the largest exponent of the variable found in the polynomial.

A linear polynomial is an expression with the variable raised to one, for example, "a times x plus b."

A quadratic polynomial includes the variable raised to the second power, like "a times x squared plus b times x plus c."

A cubic polynomial contains the variable raised to the third power, such as "a times x cubed plus b times x squared plus c times x plus d."

The coefficient is the number multiplied by the variable in each term, for example, in "four x squared," the number four is the coefficient.

You add polynomials by merging terms that have the same variables and powers, using regular addition for their coefficients.

Subtracting polynomials means you subtract the coefficients of terms that have matching variables and exponents.

To multiply polynomials, multiply every term in one polynomial by every term in the other and then add any like terms.

The zero of a polynomial is a value for the variable that makes the whole expression equal to zero.

The Factor Theorem says if a polynomial equals zero when you substitute a number for the variable, then the expression "variable minus that number" is a factor of the polynomial.

The Remainder Theorem tells us that if you divide a polynomial by "variable minus a number," the remainder is what you get when you plug that number into the polynomial.

To factorize a polynomial, rewrite it as a multiplication of simpler polynomials, just like splitting a number into its factors.

Polynomials are crucial because they help in describing patterns, solving equations, and modeling real-life scenarios in mathematics and science.

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