Find the value of k if the polynomial p(x) = 3x^3 + kx^2 + 5x - 16 is divided by (x-2) leaves a remainder -8
Answers
Step-by-step explanation:
Given:-
The polynomial p(x) = 3x^3 + kx^2 + 5x - 16 is divided by (x-2) leaves a remainder -8
To find:-
Find the value of k ?
Solution:-
Given Polynomial p(x) = 3x^3+kx^2+5x- 16
Given divisor = (x-2)
Given remainder = -8
We know that
Remainder Theorem:-
P(x) be a polynomial of the degree is greater than or equal to 1 and (x-a) is another linear polynomial ,if p(x) is divided by (x-a) then the remainder is p(a).
If p(x) is divided by (x-2) then the remainder is p(2) = -8
=> 3(2)^3 + k(2)^2 +5(2) -16 = -8
=> 3(8)+k(4)+10-16 = -8
=> 24 + 4k + 10 - 16 = -8
=> 34-16+4k = -8
=> 18+4k = -8
=> 4k = -8-18
=> 4k = -26
=> k = -26/4
=> k = -13/2
Therefore,k = -13/2
Answer:-
The value of k for the given problem is -13/2
Used formula:-
Remainder Theorem:-
P(x) be a polynomial of the degree is greater than or equal to 1 and (x-a) is another linear polynomial ,if p(x) is divided by (x-a) then the remainder is p(a).
Step-By-Step Explanation:
Given:-
The polynomial p(x) = 3x^3 + kx^2 + 5x - 16 is divided by (x-2) leaves a remainder -8
To find:-
Find the value of k ?
Solution:-
Given Polynomial p(x) = 3x^3+kx^2+5x- 16
Given divisor = (x-2)
Given remainder = -8
We know that
Remainder Theorem:-
P(x) be a polynomial of the degree is greater than or equal to 1 and (x-a) is another linear polynomial ,if p(x) is divided by (x-a) then the remainder is p(a).
If p(x) is divided by (x-2) then the remainder is p(2) = -8
=> 3(2)^3 + k(2)^2 +5(2) -16 = -8
=> 3(8)+k(4)+10-16 = -8
=> 24 + 4k + 10 - 16 = -8
=> 34-16+4k = -8
=> 18+4k = -8
=> 4k = -8-18
=> 4k = -26
=> k = -26/4
=> k = -13/2
Therefore,k = -13/2
Answer:-
The value of k for the given problem is -13/2
Used formula:-
Remainder Theorem:-
P(x) be a polynomial of the degree is greater than or equal to 1 and (x-a) is another linear polynomial ,if p(x) is divided by (x-a) then the remainder is p(a).