what value of b makes the polynomial a perfect square?

Question

X^2+bx+36

Answer 1

36 is the square of 6.  Multiply the square-root of 36 by 2.

 

6 * 2 = 12

 

b = 12

 

 

x² + 12x + 36 =

 

(x + 6)(x + 6)

Answer 2

Great job, Michael!

 

I would only add that the reason you multiply by 2 is the fact that you will have 2 middle terms when you FOIL.

(In this case, 6x + 6x, OR (-6x) +(-6x))

 

Note that the square root of any number can be either positive or negative, so +6 and -6 both work in this problem.

 

(Because (-6)*(-6) = + 36, too.)

 

The value of b could also be -12.