Question

Divide 3x2 – 11x – 4 by x – 4.

Answer 1

I hope this helps you




3x²-11x-4
_________

(x-4)


(3x+1)(x-4)
_________
(x-4)



3x+1

Answer 2

The answer is
`(3x+1)`

Explanation:

we have

`(3x^(2)-11x-4)/(x-4)`

Convert the numerator in factored form

`3x^(2)-11x-4=0`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`3x^(2)-11x=4`

Factor the leading coefficient

`3(x^(2)-11x/3)=4`

Complete the square. Remember to balance the equation by adding the same constants to each side.

`3(x^(2)-11x/3+(121/36))=4+(121/12)`

`3(x^(2)-11x/3+(121/36))=(169/12)`

`(x^(2)-11x/3+(121/36))=(169/36)`

Rewrite as perfect squares

`(x-(11/6))^(2)=(169/36)`

Square root both sides

`x-(11)/(6)=(+/-)(13)/(6)`

`x=(11)/(6)(+/-)(13)/(6)`

`x=(11)/(6)+(13)/(6)=4`

`x=(11)/(6)-(13)/(6)=-(1)/(3)`

therefore

`3x^(2)-11x-4=3(x-4)(x+(1)/(3))=(x-4)(3x+1)`

Substitute

`(3x^(2)-11x-4)/(x-4)=((x-4)(3x+1))/(x-4)=(3x+1)`