find the remainder when p(X)=x²-5x-11 is divided by x-7
Answers
Step-by-step explanation:
Given :-
p(x) = x²-5x-11
Divisor = x-7
To find :-
Find the remainder when p(x)=x²-5x-11 is divided by x-7.
Solution :-
Long Division method:-
Given that
p(x) = x²-5x-11
Divisor = x-7
On dividing p(x) by (x-7)
x-7 ) x²-5x-11 ( x+2
x²-7x
(-) (+)
________
0+ 2x -11
2x -14
(-) (+)
_________
3
_________
Quotient = x+2
Remainder = 3
Using Remainder Theorem:-
Let p(x) be a polynomial of the degree greater than or equal to 1 and (x-a) is another linear polynomial if p(x) is divided by x-a then the remainder p(a) .
Given p(x) is divided by (x-7) then the remainder is p(7)
Put x= 7 in p(x) then
p(7) = (7)²-5(7)-11
=> p(7) = 49-35-11
=> p(7) = 49-46
=> p(7) = 3
Therefore,p(7) = 3
Answer:-
The required remainder for the given problem is 3
Used formulae:-
Remainder Theorem:-
Let p(x) be a polynomial of the degree greater than or equal to 1 and (x-a) is another linear polynomial if p(x) is divided by x-a then the remainder p(a) .