Question

Use the remainder theorem to find the remainder for each of the following divisions. (x²+3x+1)/(x+2)

Answer 1

The remainder of this division is -1.

Explanation:

Given data in the question:-

Dividend=
`x^2+3x+1`

Divisor=
`x+2`

Solution:-

To find the remainder using the remainder theorem. We have to substitute -2 in the dividend and on solving that we will get the remainder.

We got -2 from the divisor when we equate the divisor to 0.

x+2=0

x=-2

`p(a)=x^2+3x+1\\`

Substituting -2 in above written equation.

`p(-2)=(-2)^2+3(-2)+1\\p(-2)=4-6+1\\p(-2)=5-6\\p(-2)=-1`