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Polynomials — Class 9 CBSE Mathematics MCQs with Solutions
Free Class 9 CBSE Mathematics Polynomials MCQs with step-by-step solutions. Practise online on Prepizo — no login needed.
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Sample questions with solutions
Q1 — easy
Degree of a non-zero constant polynomial is:
A. 0 ✓ Correct
B. 1
C. Undefined
D. Any real number
Solution: A constant polynomial like c = c·x⁰ has degree 0.
Q2 — easy
Degree of the zero polynomial is:
A. 0
B. 1
C. Undefined ✓ Correct
D. Any positive integer
Solution: The degree of zero polynomial 0 is not defined.
Q3 — easy
Zeros of the polynomial p(x) = x² − 5x + 6 are:
A. 2 and 3 ✓ Correct
B. −2 and −3
C. 1 and 6
D. −1 and −6
Solution: x² − 5x + 6 = (x − 2)(x − 3) = 0 → x = 2, 3.
Q4 — easy
If x + 1 is a factor of p(x) = x³ + x² + x + k, then k =
A. 1
B. −1 ✓ Correct
C. 0
D. 2
Solution: By Factor Theorem, p(−1) = 0 → (−1)³ + (−1)² + (−1) + k = 0 → −1 + 1 − 1 + k = 0 → k = 1. Wait: -1+1-1+k=0 => k=1.
Q5 — easy
If x + y + z = 0, then x³ + y³ + z³ =
A. 0
B. 3xyz ✓ Correct
C. xyz
D. 3(x + y + z)
Solution: Using identity x³ + y³ + z³ − 3xyz = (x+y+z)(x²+y²+z²−xy−yz−zx) = 0.
Q6 — easy
Find remainder when p(x) = x³ − 3x² + 3x − 1 is divided by (x − 1):
A. 0 ✓ Correct
B. 1
C. −1
D. 2
Solution: p(1) = 1³ − 3(1)² + 3(1) − 1 = 1 − 3 + 3 − 1 = 0.
Q7 — easy
Coefficient of x² in polynomial 2 − x² + x³ is:
A. 1
B. −1 ✓ Correct
C. 2
D. 0
Solution: The x² term is −1·x², so coefficient = −1.
Q8 — easy
Factorize x² − 25 using algebraic identity:
A. (x − 5)²
B. (x + 5)(x − 5) ✓ Correct
C. (x + 25)(x − 1)
D. (x + 5)²
Solution: a² − b² = (a+b)(a−b) → x² − 5² = (x+5)(x−5).
Q9 — easy
Evaluate: (102)³ using algebraic identities:
A. 1061208 ✓ Correct
B. 1060000
C. 1061200
D. 1040400
Solution: (100 + 2)³ = 100³ + 2³ + 3(100)(2)(102) = 1000000 + 8 + 61200 = 1061208.
Q10 — easy
Polynomial of degree 3 is called a:
A. Linear polynomial
B. Quadratic polynomial
C. Cubic polynomial ✓ Correct
D. Biquadratic polynomial
Solution: A degree 3 polynomial is a cubic polynomial.
Q11 — easy
Which of the following expressions is a polynomial in one variable?
A. x + (1/x)
B. √x + 2
C. x² + 3x + 5 ✓ Correct
D. x + y + z
Solution: Exponent powers of variable x are non-negative whole numbers in x² + 3x + 5.
Q12 — easy
If p(x) = 5x − 4x² + 3, find p(−1):
A. 6
B. −6 ✓ Correct
C. −2
D. 2
Solution: p(−1) = 5(−1) − 4(−1)² + 3 = −5 − 4 + 3 = −6.
Q13 — easy
Expand: (x + 2y + 4z)² =
A. x² + 4y² + 16z² + 4xy + 16yz + 8zx ✓ Correct
B. x² + 2y² + 4z² + 2xy + 4yz + 4zx
C. x² + 4y² + 8z² + 4xy + 8yz + 4zx
D. x² + y² + z² + xy + yz + zx
Solution: (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca.
Q14 — easy
Zero of linear polynomial p(x) = 2x + 5 is:
A. 5/2
B. −5/2 ✓ Correct
C. −2/5
D. 2/5
Solution: 2x + 5 = 0 → x = −5/2.
Q15 — medium
Value of 99² − 1² is:
A. 9800 ✓ Correct
B. 9900
C. 10000
D. 9700
Solution: (99+1)(99−1) = 100 × 98 = 9800.