Question

(x^3 - 7x + 2)divided by (x+2)using long division method

Answer 1

Answer:

We divide 3x

3

+4x

2

+x+7 by (x

2

+1) as shown in the above image:

From the division, we observe that the quotient is 3x+4 and the remainder is −2x+3.

We know that the division algorithm states that:

Dividend=Divisor×Quotient+Remainder

We apply the division algorithm to check the answer as follows:

Dividend=Divisor×Quotient+Remainder

3x

3

+4x

2

+x+7=[(x

2

+1)(3x+4)]−2x+3

3x

3

+4x

2

+x+7=(3x

3

+4x

2

+3x+4)−2x+3

3x

3

+4x

2

+x+7=3x

3

+4x

2

+3x−2x+4+3

3x

3

+4x

2

+x+7=3x

3

+4x

2

+x+7

Henceverified.