Question

On dividing the polynomial x³ -5x² + 6x -4 by a polynomial g(x), quotient and remainder are (x –3) and (– 3x + 5) respectively. Find g(x).

Answer 1

Firstly write the given values in division algorithm and then find the value of g (x). Now further divide numerator of g(x)  by denominator and simplify it to get g(x).

Division algorithm:
Dividend=  Divisor × Quotient + Remainder
p(x) = q(x) × g(x) + r(x)

Given:
p(x) =  x³ -5x²  +  6x - 4
q(x) = (x-3)
r(x)= (-3x+5)

Put the values of p(X), q(x) & r(x) in Division algorithm.

p(x) = q(x) × g(x) + r(x)
x³ -5x² + 6x - 4  =  (x-3) × g(x) +(-3x+5)
x³ -5x² + 6x - 4 +3x- 5  =  (x-3) × g(x)
x³ -5x² + 6x +3x- 5 - 4 =  (x-3) × g(x)
x³ -5x² + 9x - 9 =  (x-3) × g(x)

g(x) = x³ -5x² + 9x - 9 / (x-3)

Divide x³ -5x² + 9x - 9 by (x-3)
x-3 ) x³ -5x² + 9x - 9(x²-2x+3
x³ -3x²
(-) (+)
---------------
-2x²+9x -9
-2x²+6x
(+) (-)
----------------------
3x -9
3x -9
(-) (-)
----------------------
0

On dividing x³ -5x² + 9x - 9 by x-3, we get quotient g(x)= x²-2x+3

Hence, g(x)= x²-2x+3

HOPE THIS WILL HELP YOU....

Answer 2

HET GUYS HERE IS MY ANSWER

WE KNOW THAT,

p(x)= q(n)×g(n) +r(n)

x³-5x²+6x-4 = (x-3)*g(m)+ (-3x+5)

x³-5x+6x-4+3n-5=(x-3)*g(n)

x³-5x+9n-9= (x-3)*g(n)

x³-5x²+9n-9