POLYNOMIALS

(বহুপদী)

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🔹 Important Topics in this Chapter

• Definition of Polynomial
• Degree of a Polynomial
• Zeros of a Polynomial
• Relationship between Zeros & Coefficients
• Graphical Representation
• Factor Theorem
• Remainder Theorem

👉 This chapter carries sure 8–10 marks in HSLC

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🟢 1. What is a Polynomial?

✅ English:

A polynomial in one variable x is an expression of the form$$a_nx^n + a_{n-1}x^{n-1} + \dots + a_1x + a_0$$an​xn+an−1​xn−1+⋯+a1​x+a0​

where $a_n, a_{n-1}, …, a_0$an​,an−1​,…,a0​ are real numbers and $a_n \ne 0$an​=0.

✅ অসমীয়া:

এটা চলকযুক্ত বহুপদী হৈছে$$a_nx^n + a_{n-1}x^{n-1} + \dots + a_1x + a_0$$an​xn+an−1​xn−1+⋯+a1​x+a0​

য’ত সকলো গুণাঙ্ক বাস্তৱ সংখ্যা আৰু $a_n \ne 0$an​=0।

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🟢 2. Degree of a Polynomial

English:

The highest power of the variable in a polynomial is called its degree.

Assamese:

বহুপদীত চলকৰ সৰ্বাধিক ঘাত-ক বহুপদীৰ ঘাত (Degree) বোলা হয়।

Examples:

Polynomial	Degree
5x² + 3x + 1	2
7x³ − x	3
9	0

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🟢 3. Zeros of a Polynomial

English:

A real number α is called a zero of polynomial p(x) if$$p(\alpha) = 0$$p(α)=0

Assamese:

যদি p(α) = 0 হয়, তেন্তে α-ক বহুপদীৰ শূন্য (Zero) বোলা হয়।