pl solve it its urgent plz plz plz
x3-3x2+x+2divided by x2-x+1
Answers
Answer:
g(x) = x² - x + 1
Step-by-step explanation:
On dividing x3-3x2+x+2 by a polynomial g(x),the quotient and remainder were x-2 and -2x+4 respectively.find g(x)
f(x) = x³ - 3x² + x + 2
q(x) = x - 2
let say
g(x) = ax² + bx + c
r = - 2x + 4
f(x) = g(x)q(x) + r
=> x³ - 3x² + x + 2 = (ax² + bx + c)(x - 2) + (-2x + 4)
=> x³ - 3x² + x + 2 = ax³ + x²(b - 2a) + x(c - 2b) -2c -2x + 4
=> x³ - 3x² + x + 2 = ax³ + x²(b - 2a) + x(c - 2b - 2) + (-2c + 4)
Equating Power terms
a = 1
b - 2a = - 3 => b -2 = -3 => b = -1
c - 2b - 2 = 1 => c + 2 - 2 = 1 => c = 1
or -2c + 4 = 2 => -2c = -2 => c = 1
g(x) = x² - x + 1
Mark me as brainliest because it is ur urgent question
Answer:
x^2-x+1
Step-by-step explanation:
I think it's helpful to you
follow me
for full division search in google plss
Mark as brainliest