🔹 Question 1
Which of the following expressions are polynomials in one variable and which are not? State the reason.
তলত দিয়া কোনবোৰ এটা চলকৰ বহুপদী আৰু কোনবোৰ নহয়? কাৰণ লিখা।
(i) 4x² − 3x + 7
✔ Polynomial / বহুপদী
Reason / কাৰণ :
- Only one variable (x)
- Powers of x are whole numbers (2, 1, 0)
(ii) y² + √y
❌ Not a polynomial / বহুপদী নহয়
Reason / কাৰণ :
√y = y¹ᐟ² (fraction power)
Fraction power is not allowed in polynomials.
(iii) 5
✔ Polynomial / বহুপদী
Reason / কাৰণ :
- Constant term
- Can be written as 5 = 5x⁰
- Degree = 0
(iv) 3x³ − 4x + 1/x
❌ Not a polynomial / বহুপদী নহয়
Reason / কাৰণ :
1/x = x⁻¹ (negative power)
Negative powers are not allowed.
(v) 2x + 3y
❌ Not a polynomial in one variable
(But it is a polynomial in two variables)
কাৰণ :
দুটা চলক আছে (x আৰু y)
🔹 Question 2
Find the degree of the following polynomials.
তলত দিয়া বহুপদীবোৰৰ degree উলিয়াওক।
(i) 7x³ + 5x² − x + 9
Highest power of x = 3
👉 Degree = 3
(ii) 4 − x
Highest power of x = 1
👉 Degree = 1
(iii) 9x⁵ − 2x² + x
Highest power of x = 5
👉 Degree = 5
(iv) 8
8 = 8x⁰
👉 Degree = 0
🔹 Question 3
Find the value of the polynomial 2x² − 3x + 1 at x = 2.
x = 2 হলে 2x² − 3x + 1 ৰ মান উলিয়াওক।
Solution / সমাধান
Given polynomial:
2x² − 3x + 1
Put x = 2
= 2(2)² − 3(2) + 1
= 2 × 4 − 6 + 1
= 8 − 6 + 1
= 3
👉 Answer / উত্তৰ : 3
🔹 Question 4
Find the zero of the polynomial x − 5.
x − 5 বহুপদীৰ zero উলিয়াওক।
Solution / সমাধান
Zero means value = 0
x − 5 = 0
x = 5
👉 Zero = 5
🔹 Question 5
Find the zero of the polynomial 3x + 6.
3x + 6 বহুপদীৰ zero উলিয়াওক।
Solution / সমাধান
3x + 6 = 0
3x = −6
x = −2
👉 Zero = −2
🌟 VERY IMPORTANT EXAM TIPS
✔ Polynomial never has √x or 1/x
✔ Degree = highest power
✔ Constant → degree 0
✔ Zero means polynomial value becomes 0
❌ COMMON STUDENT MISTAKES
❌ Writing √x as polynomial
❌ Taking negative power
❌ Forgetting constant degree