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Class 9 Degree and Types of Polynomials — practice questions with answers

Polynomials · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. What is the degree of the polynomial 5x³ + 2x² - 7x + 4?
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Answer: C) 3
The degree of a polynomial in one variable is the highest power of the variable. The highest power here is 3 (in 5x³).
2. Which of the following is a linear polynomial in one variable?
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Answer: B) 3x - 8
A linear polynomial has degree 1. 3x - 8 has highest power 1.
3. What is the degree of the polynomial 3x⁰ + 0x² + 0x⁴ (after simplifying)?
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Answer: A) 0
0x² and 0x⁴ are zero, so the polynomial simplifies to 3, a non-zero constant of degree 0.
4. A polynomial in x has 4 terms and its highest power is 5.
However, when arranged in standard form, the term in x⁵ cancels with another x⁵ term, leaving 3 terms with highest power 3.
What is the degree and type (by terms) of the final polynomial?
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Answer: B) Degree 3, trinomial
After the x⁵ terms cancel, the highest remaining power is 3 (degree 3) and there are 3 terms (trinomial).
5. Asha forms a polynomial by adding a cubic polynomial and a different cubic polynomial.
She notices that the leading x³ terms are negatives of each other and cancel.
The remaining highest power is x².
What is the degree of Asha's resulting polynomial?
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Answer: B) 2
Although both are cubic (degree 3), their x³ terms cancel on addition. The next highest power present is 2, so the resulting polynomial has degree 2.
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