Q1.DegreeEasy · 1m
What is the degree of the polynomial 4x³ − 2x + 7?
Answer: 3 — the highest power of x is 3.
Class 9 · Maths · Important Questions
Polynomials — Important Questions
Q2.ZeroesEasy · 2m
Find the zero of the polynomial p(x) = 2x + 3.
Answer: Put p(x) = 0: 2x + 3 = 0 ⇒ x = −3/2.
Q3.Remainder TheoremMedium · 2m
Find the remainder when p(x) = x³ + 3x² + 3x + 1 is divided by (x + 1).
Answer: By the remainder theorem, remainder = p(−1) = −1 + 3 − 3 + 1 = 0.
Q4.IdentitiesMedium · 2m
Expand (2x + 3y)² using a standard identity.
Answer: (a + b)² = a² + 2ab + b² ⇒ 4x² + 12xy + 9y².
Q5.Factor TheoremMedium · 3m
Using the factor theorem, check whether (x − 2) is a factor of x³ − 3x² + 4.
Answer: p(2) = 8 − 12 + 4 = 0, so (x − 2) is a factor.
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