Question

Which is equivalent to the expression? x2 + 6x + 4 A) (x + 3)2 + 5 B) (x + 3)2 − 5 C) (x − 3)2 + 5 D) (x − 3)2 − 5

Answer 1

Answer:

Step-by-step explanation:

(x + 3)² − 5   because :

(x + 3)² − 5 = x² +6x+9 -5 =x²+6x+4

Answer 2

Answer:

B) $(x + 3)^2 - 5$

Step-by-step explanation:

the equation is: $x^2 + 6x + 4$

we have an equation of the form

$ax^2+bx+c$

where

$a=1,b=6,c=4$

and we must complete the square to obtain a perfect square binomial,

we must add and substract the following:

$(\frac{b}{2a} )^2$

which is:

$(\frac{6}{2*1} )^2=3^2$

and then the equation becomes:

$x^2 + 6x + 4+3^2-3^2$

where the terms $x^2+6x+3^2$ are the components of the perfect square binomial: $(x+3)^2$

and thus, the equation now is:

$(x+3)^2+4-3^2\\=(x-3)^2+4-9\\=(x+3)^2-5$

the answer is: B) $(x + 3)^2 - 5$