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Factor and Remainder theorem

1.  Remainder theorem

If a polynomial f(x) is divided by (x – α) then remainder = f(α)

Example: Find the remainder (Without division) on dividing f(x) by (x + 3) where f(x) = 2x2 – 7x – 1

Solution:-

X + 3 = 0    or,  x = -3

put x = -3 in f(x)

f(-3) = 2(-3)(-3) – (-3) – 1 = 20

Hence, remainder is 20.

2. Factor theorem

(x- α) is a factor of the polynomial f(x) if and only if f(α) = 0

Example: Show that (x – 5) is factors of f(x) where f(x) = 2x2 – 11x + 5.

Solution:-

x – 5 = 0   or, x = 5

put x = 5 in f(x)

f(5) = 2(5)(5) – 11(5) + 5 = 50 – 50 = 0

Hence (x – 5) is the factor.

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With the first Bharatiya Janata Party-led government in West Bengal having already taken charge with Suvendu Adhikari as the first BJP Chief Minister, Siddhartha Majumdar, the chairman of the West Bengal School Service Commission (WBSSC), an autonomous body under the State Education Department, has tendered his resignation on Tuesday.

WBBSE माध्यमिक परिणाम 2026 लाइव: WB कक्षा 10वीं के परिणाम आज सुबह 9.30 बजे wbbse.wb.gov.in पर जारी होंगे। WBBSE मध्यमा परिणाम 2026 लाइव: पश्चिम बंगाल माध्यमिक शिक्षा बोर्ड ने 8 मई, 2026 को WBBSE माध्यमिक परिणाम 2026 जारी किया। WB कक्षा 10वीं के परिणाम आज सुबह 9.30 बजे घोषित किए गए। जो उम्मीदवार परीक्षा के लिए उपस्थित हुए हैं, वे WBBSE की आधिकारिक वेबसाइट wbbse.wb.gov.in पर परिणाम देख सकते…

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