Question

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

Answer 1

Answer:

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

Step-by-step 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

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

$x=(-11/8)(+/-)\frac{5}{8}$

$x=(-11/8)+\frac{5}{8}=-\frac{6}{8}=-\frac{3}{4}$

$x=(-11/8)-\frac{5}{8}=-\frac{16}{8}=-2$

therefore

$4x^{2} +11x+6=4(x+\frac{3}{4})(x+2)=(4x+3)((x+2)$

the answer is

$(4x+3)((x+2)$