On dividing x^3-8x3^2+20x-10 by a polynomial g(n) the quotient and the reminder where x-4 and 6 respectively find g(n)

Open in App

Solution

according to division algorithm
Dividend = Divisor × Quotient+ Remainder
p(x) = g(x) × q(x) + r(x),
plug the value in formula we get
x^3 – 8x^2 + 20x - 10 = g(x) (x-4) + 6
x^3 – 8x^2 + 20x - 16=g(x) (x-4)
simplify
(x^3 – 8x^2 + 20x - 16)/(x-4) = g(x)
g(x)= x^2-4x+4

Suggest Corrections

Similar questions

Q. On dividing a polynomial

3 x^{3} + 4 x^{2} + 5 x - 13

by a polynomial g(x), the quotient and the reminder were

3 x + 10

and

16 x - 43

respectively. Find the polynominalg(x).

Q. Divide the first polynomial by the second polynomial and express as Divided = Divisor x quotient + Reminder

x^{3} - 5 x^{2} + 4 x + 8; x + 2

Q. On dividing polynomial

x^{3} - 3 x^{2} + x + 2

by a polynomial

g (x)

, the quotient and remainder were

x - 2

and

- 2 x + 4

, respectively. Find

g (x)

Question 4
On dividing $x^{3} - 3 x^{2} + x + 2$ by a polynomial g(x), the quotient and remainder were $x - 2$ and $- 2 x + 4$ , respectively. Find g(x).

On dividing $3 x^{3} + x^{2} + 2 x + 5$ by a polynomial g(x), the quotient and remainder are (3x-5) and (9x+10) respectively. Find g(x).

Join BYJU'S Learning Program

On dividing x^3-8x3^2+20x-10 by a polynomial g(n) the quotient and the reminder where x-4 and 6 respectively find g(n)

according to division algorithm Dividend = Divisor × Quotient+ Remainder p(x) = g(x) × q(x) + r(x), plug the value in formula we get x^3 – 8x^2 + 20x - 10 = g(x) *(x-4) + 6 x^3 – 8x^2 + 20x - 16=g(x) *(x-4) simplify (x^3 – 8x^2 + 20x - 16)/(x-4) = g(x) g(x)= x^2-4x+4

according to division algorithm
Dividend = Divisor × Quotient+ Remainder
p(x) = g(x) × q(x) + r(x),
plug the value in formula we get
x^3 – 8x^2 + 20x - 10 = g(x) (x-4) + 6
x^3 – 8x^2 + 20x - 16=g(x) (x-4)
simplify
(x^3 – 8x^2 + 20x - 16)/(x-4) = g(x)
g(x)= x^2-4x+4