Find the remainder (without division) when 8x2 +5x + 1 is divisible by x - 10
Answers
Given :- Find the remainder (without division) when 8x² +5x + 1 is divisible by x - 10 ?
Solution :-
we know that, when p(x) is divided by (x - a) , the remainder will be p(a) .
so, dividing 8x² + 5x + 1 by (x - 10) ,
→ p(x) = 8x² + 5x + 1
→ p(10) = 8(10)² + 5(10) + 1
→ p(10) = 8 * 100 + 50 + 1
→ p(10) = 800 + 51
→ p(10) = 851 (Ans.)
hence, when 8x² +5x + 1 is divisible by x - 10 remainder will be 851 .
Learn more :-
JEE mains Question :-
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. Find all the zeroes of the polynomial x4
– 5x3 + 2x2+10x-8, if two of its zeroes are 4 and 1.
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Given : 8x² +5x + 1 is divided by x - 10
To Find : Remainder
Solution:
Using remainder theorem :
if polynomial p(x) is divided by x - m
then remainder is p(m)
and if p(m) = 0 then (x - m) is a factor
p(x) = 8x² +5x + 1
divided by x - 10
Hence m = 10
so remainder =p(10)
p(10) =8(10)² +5(10) + 1 = 851
Verification by division
8x + 85
x - 10 _| 8x² +5x + 1 |_
8x² - 80x
_______
85x + 1
85x - 850
__________
851
Verified that remainder is 851
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