Jan 7, 2020
Remainder and Factor theorem | Mathematics class 10
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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