Question

How would you put this expression in factored form? 4x2 + 11x + 6

Answer 1

Its (4x+3)(x+2) 100%

Explanation:

Answer 2

we have

`4x^(2) +11x+6`

Equate the expression to zero

`4x^(2) +11x+6=0`

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

`4x^(2) +11x=-6`

Factor the leading coefficient

`4(x^(2) +(11x/4))=-6`

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

`4(x^(2) +(11x/4)+(121/64))=-6+(121/16)`

`4(x^(2) +(11x/4)+(121/64))=(25/16)`

`(x^(2) +(11x/4)+(121/64))=(25/64)`

Rewrite as perfect squares

`(x+(11/8))^(2)=(25/64)`

Square root both sides

`x+(11/8)=(+/-)\sqrt{(25)/(64)}`

`x=(-11/8)(+/-)(5)/(8)`

`x=(-11/8)+(5)/(8)=-(6)/(8)=-(3)/(4)`

`x=(-11/8)-(5)/(8)=-(16)/(8)=-2`

therefore

`4x^(2) +11x+6=4(x+(3)/(4))(x+2)=(4x+3)((x+2)`

the answer is

`(4x+3)((x+2)`