Question

What is the quotient when 2x3 + x + 3 is divided by x + 1?

a. 2x2 + 2x + 3
b. 2x2 − 2x + 3
c. + 2x + 3 − 6 over the quantity of x plus 1
d. 2x2 − 2x + 3 + 6 over the quantity of x plus 1

Answer 1

To find the quotient when
`2x^3+x+3` is divided by
`x+1` you have to do such steps:

1. Multiply
`x+1` by
`2x^2` and subtract the result from the
`2x^3+x+3` in order to eliminate
`2x^3` term:

`2x^3+x+3-2x^2(x+1)=2x^3+x+3-2x^2-2x^2=-2x^2+x+3.`

2. Multiply
`x+1` by
`-2x` and subtract the result from the
`-2x^2+x+3` in order to eliminate
`-2x^2` term:

`-2x^2+x+3-(-2x)(x+1)=-2x^2+x+3+2x^2+2x=3x+3.`

3. Multiply
`x+1` by
`3` and subtract the result from the
`3x+3` in order to eliminate
`3x` term:

`3x+3-3(x+1)=3x+3-3x-3=0.`

4. Now you can write that

`2x^3+x+3=(x+1)(2x^2-2x+3).`

The quotient is
`2x^2-2x+3` and the remainder is 0.

Answer: correct choice is B

Answer 2

I hope this helps you