Class 9 • Maths • Chapter 2
Polynomials
True & False Quiz
Degree. Zero. Remainder.
✓True
✗False
25
Questions
|
Ch.2
Chapter
|
IX
Class
Why True & False for Polynomials?
How this format sharpens your conceptual clarity
🔵 Polynomials are the algebraic language of curves and equations — understanding zeroes, factors, and the remainder theorem directly feeds into Class X and XI.
✅ T/F questions target degree, types (monomial, binomial, trinomial), and the two critical theorems: Remainder and Factor.
🎯 Remainder Theorem: p(a) is the remainder when p(x) is divided by (x−a) — if p(a)=0, then (x−a) is a factor (Factor Theorem).
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
All algebraic expressions are polynomials.
Q 2
\(x^3 + 2x^2 - x + 7\) is a cubic polynomial.
Q 3
A monomial is a polynomial with exactly one term.
Q 4
The degree of the polynomial \(5x^4 + 2x^2 + x + 1\) is 2.
Q 5
The coefficient of \(x\) in \(7x - 5x^2 + 4\) is 7.
Q 6
\(x^2 - 4x + 2\) has degree 2.
Q 7
The polynomial 3 is a zero polynomial.
Q 8
\(2xy + 3x\) is a polynomial in one variable.
Q 9
Every polynomial of degree 1 is called a linear polynomial.
Q 10
The zero of the polynomial \(x + 5\) is -5.
Q 11
The number of zeroes of a quadratic polynomial is always two.
Q 12
The standard form of a polynomial arranges terms in decreasing powers of the variable.
Q 13
The remainder theorem applies only to linear divisors.
Q 14
A binomial has two unlike terms.
Q 15
If \((x - a)\) is a factor of polynomial \(f(x)\), then f(a) = 0.
Q 16
The polynomial \(x^4 + x^2 + 1\) is a quadratic polynomial.
Q 17
The value of a polynomial at a point is found by substituting the variable by that value.
Q 18
The product of two linear polynomials is always quadratic.
Q 19
Algebraic identity \((a + b)^2 = a^2 + 2ab + b^2\) is a polynomial equality.
Q 20
Zero polynomial has no degree.
Q 21
A trinomial must have degree 3.
Q 22
Every constant polynomial is of degree zero.
Q 23
If \(p(x) = x^2 + 1\), then \(p(0) = 1\).
Q 24
The sum of two polynomials is always a polynomial.
Q 25
A term like \(\frac{2}{x}\) is allowed in a polynomial.
Key Takeaways — Polynomials
Core facts for CBSE Boards & exams
1
Degree = highest power of the variable; degree of constant polynomial is 0; degree of zero polynomial is undefined.
2
Linear: degree 1; Quadratic: degree 2; Cubic: degree 3.
3
Remainder Theorem: remainder of p(x) ÷ (x−a) equals p(a).
4
Factor Theorem: (x−a) is a factor of p(x) iff p(a) = 0.
5
Identity: (a+b)² = a²+2ab+b²; (a−b)² = a²−2ab+b²; a²−b² = (a+b)(a−b).
6
(a+b+c)² = a²+b²+c²+2ab+2bc+2ca — six terms total.