Question

What is the quotient when −3x3 + 5x + 14 is divided by x − 2?

−3x2 − 6x − 7
− 3x2 − x + 12
−3x2 + 6x − 7 + 28 over the quantity of x minus 2
−3x2 − x + 12 + 28 over the quantity of x minus 2

Answer 1

The answer is A. -3x2 - 6x - 7

Answer 2

`-3x^(2) -6x-7`

Explanation:

The given expression is :

`(-3x^(3)+5x+14)/(x-2)`

Factoring
`-3x^(3)+5x+14`

Factor out common term -1

`3x^(3)-5x-14`

Now dividing leading coefficients of numerator and divisor.

`(3x^(3))/(x)=3x^(2)`

Multiplying x-2 with
`3x^(2)` =
`3x^(3)-6x^(2)`

Subtracting
`3x^(3)-6x^(2)` from
`3x^(3)-5x-14`

we get
`6x^(2) -5x-4`

Therefore,
`(-3x^(3)+5x+14)/(x-2)` =
`3x^(2) +(6x^(2)-5x-14)/(x-2)`

Now repeating these same steps until (x-2) is factored out, we get the quotient as :

`-3x^(2) -6x-7`