Factor completely.
x^2 + 5x + 6

A) (x- 3)(x + 3)
B) (x- 1)(x + 6)
C) (x + 3)(x + 2)
D) (x + 5)(x + 1)

Question

Factor completely.
x^2 + 5x + 6

A) (x- 3)(x + 3)
B) (x- 1)(x + 6)
C) (x + 3)(x + 2)
D) (x + 5)(x + 1)

campbell_st · Answer

well you need to find the factors of 6 that add to 5... 

in general if a quadratic can be factored

$$x^2 + bx + c $$

the factors of c need to add to the value of b

anonymous · Answer

so what are you saying I need to do? I dont really understand. @campbell_st

campbell_st · Answer

ok... can you indentify the factors of 6... 

there are only 2 pairs...

anonymous · Answer

is it 3?

anonymous · Answer

im sorry if its not im really bad at this... :(

campbell_st · Answer

ok... find 2 numbers that multiply to 6...

anonymous · Answer

well 6 and 1 make 6 and 3 and 2 make 6

campbell_st · Answer

great so 1 and 6 are factors of 6

and 3 and 2 are also factors of 6

which pair of factors add to 5...?

anonymous · Answer

3 and 2!

campbell_st · Answer

great so its written as 

(x + factor 1)(x + factor 2)

so 

$$x^2 + 5x + 6 = (x + 3)(x + 2)$$

to check you can split the 1st brackets 

$$x(x +2) + 3(x + 2)$$

by distributing and collecting like terms you get the original equation

anonymous · Answer

oh wow thank you soo much!!! that really really helped me!!! @campbell_st