Question

on dividing x3-3x2+x+2 by a polynomial g(x) the quotient and remainder were x-3 and 4 respectively find g of x​

Answer 1

Answer:

g(x)=x

2

−x+1

Step-by-step explanation:

Dividend =p(x)=x

3

−3x

2

+x+2

Quotient =q(x)=x−2

Remainder =r(x)=2x+4

By division algorithm, p(x)=q(x)g(x)+r(x)

⇒g(x)=

q(x)

p(x)−r(x)

⇒g(x)=

x−2

x

3

−3x

2

+x+2+2x−4

⇒g(x)=

x−2

x

3

−3x

2

+3x−2

So, g(x)=x

2

−x+1

Answer 2

Given:

Dividend = x³ - 3x² + x + 2

Quotient = x - 3

Reamainder = 4

To find:

Divisor g(x)

Solution:

Dividend = Divisor × Quotient + Remainder

x³ - 3x² + x + 2 = g(x) × (x - 3) + 4

x³ - 3x² + x - 2 = g(x) × (x - 3)

g(x) = (x³ - 3x² + x - 2) / (x - 3)

x - 3) x³ - 3x² + x - 2 ( x² + 1

        x³ - 3x²    ↓   ↓      

       (-)  (+)                

       0   0      x - 2

                     x - 3

                  (-)  (+)    

                          1

There is some error in the given data because we are getting remainder = 1.

The given data must be

Dividend = x³ - 3x² + x + 2

Quotient = x - 3

Reamainder = 5

Dividend = Divisor × Quotient + Remainder

x³ - 3x² + x + 2 = g(x) × (x - 3) + 5

x³ - 3x² + x - 3 = g(x) × (x - 3)

g(x) = (x³ - 3x² + x - 3) / (x - 3)

x - 3) x³ - 3x² + x - 3 ( x² + 1

        x³ - 3x²    ↓   ↓      

       (-)  (+)                

       0   0      x - 3

                     x - 3

                  (-)  (+)    

                          0

So, g(x) = x² + 1