When 2x^3-9x^2+10x-p is divided by (X+1),the remainder is -24.find the value of p only answer
When 2x^3-9x^2+10x-p is divided by (X+1),the remainder is -24.find the value of p only answer
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Answer:
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Step-by-step explanation:
Given polynomial is p(x)=2x³-9x²+10x-p
The divisor=x+1
Remainder=-24
We know that by the remainder theorem
If p(x) is divided by (x-a) then the remainder is p(a).
the given polynomial is divided by(x+1) then the remainder is p(-1).
according to the problem remainder is p(-1)=-24
p(-1)=2(-1)³-9(-1)²+10(-1)-p=-24
=>2(-1)-9(1)+10(-1)-p=-24
=>-2-9-10-p=-24
=>-21-p=-24
=>-p=-24+21
=>-p=-3
=>p=3
The value of p =3
Remainder theorem:-
Let p(x) be a polynomial of the degree greater than or equal to 1 and p(x) is divided by another linear polynomial (x-a) then the remainder is p(a).