Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Factor completely and then place the factors in the proper location on the grid. b 2 + 12b + 32

Answer 1

(x + 4)(x + 8)

That's your answer!!

Answer 2

b² +12b +32 = (b+4)(b+8)

Explanation:

The product of binomial factors (x+a) and (x+b) is ...

(x+a)(x+b) = x² +ax +bx +ab

= x² + (a+b)x + ab

That is, the coefficient of x is the sum of factors of the constant term.

In order to determine "a" and "b", you can look at the factors of 32 and see which pair has a sum that is 12.

32 = 1×32 = 2×16 = 4×8

The last factor pair has a sum that is 12, so your factorization can be

b² +12b +32 = (b+4)(b+8)