Question

What is the quotient (3x2 + 8x − 3) ÷ (x + 3)?

Answer 1

3x−1

Explanation:

3x^2+8x−3/x+3

=3x2+8x−3/x+3

=(3x−1)(x+3)/x+3

=3x−1

Answer 2

3x-1

Explanation:

We have the following expression:

`(3x^2+8x-3)/(x+3)`

Equating this equal to zero and completing the square then to get:

`3x^2+8x-3=0`

Arranging the terms which contain the same variable and moving the constant to the opposite side of the equation:

`3x^2+8x=3`

Factorize the leading coefficient:

`3(x^2+(8x)/(3) )=3`

Now complete the square and do not forget to balance the equation by adding the same constants to each side.

`3(x^2+(8x)/(3) +(16)/(9) )=3+(16)/(3)`

`3(x^2+(8x)/(3) +(16)/(9) )=(25)/(3)`

`(x^2+(8x)/(3) +(16)/(9) )=(25)/(9)`

Re-writing it as perfect square:

`(x+(4)/(3) )^2=(25)/(9)`

Taking square root at both sides to get:

`x+(4)/(3) =+-(5)/(3)`

`x=-(4)/(3) +(5)/(3) ,x=-(4)/(3) -(5)/(3)`

`x=(1)/(3) , x=-3`

So,
`3x^2+8x-3=3(x-(1)/(3))(x+3) =(3x-1)(x+3)`

Substiting it:

`(3x^2+8x-3)/(x+3)` =
`((3x-1)(x+3))/((x+3)) = (3x-1)`