Question

7. If  p(x) = x³+x²-2x+3 and g(x)=x+3, find the quotient and remainder on dividing p(x) by g (x). Also verify the division algorithm​

Answer 1

Answer:

answer for the given problem is given

Answer 2

Answer:

Quotient= x² -2x +4

Remainder = -9

Step-by-step explanation:

Concept= Division

Given= Two functions

To find = The quotient and remainder.

Explanation=

We have been the problem as p(x) = x³+x²-2x+3 and g(x)=x+3, find the quotient and remainder on dividing p(x) by g  (x). Also verify the division algorithm​.

So p(x) = x³+x²-2x+3 and g(x)=x+3.

We need to find the quotient and remainder when p(x)/g(x).

Doing division by long method:

x + 3 | x³+ x² - 2x + 3 | x² -2x +4

         x³ + 3x²

        -     -

              -2x² - 2x

              -2x² - 6x

              +      +

                        4x + 3

                         4x +12

                       -       -

                               -9

Therefore Quotient= x² -2x +4

Remainder = -9

Dividend= x³+x²-2x+3

Divisor = x + 3

Verifying Division algorithm:

Dividend = divisor*quotient + remainder

               = (x + 3)*(x² -2x +4) + (-9)

               = x(x² -2x +4) +3(x² -2x +4) -9

               = x³ -2x² + 4x + 3x² - 6x + 12 - 9

               =  x³+x²-2x+3

Hence the dividend is coming equal to  x³+x²-2x+3. So our result is correct.

Quotient= x² -2x +4

Remainder = -9

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