Question

What missing number would complete the factorization?

k2 + 5k + 6 = (k + 2)(k + ?)

A. 3
B. 6
C. 12
D. 4

Answer 1

This is the answer for your question above

Answer 2

A. 3

Explanation:

`k^2+5k+6=k^2+2k+3k+6=k(k+2)+3(k+2)\\\\=(k+2)(k+3)`

Other method:

`k^2+5k+6=(k+2)(k+x)\qquad\text{use}\ FOIL\\\\k^2+5k+6=(k)(k)+(k)(x)+(2)(k)+(2)(x)\\\\k^2+5k+6=k^2+kx+2k+2x\\\\k^2+5k+6=k^2+(x+2)k+2x\Rightarrow x+2=5\ \wedge\ 2x=6\\\\x+2=5\qquad\text{subtract 2 from both sides}\\x=3\\\\2x=6\qquad\text{divide both sides by 2}\\x=3`