SOLUTION: Would you please show me the STEPS to factor the following: 6x^2+12x+6. I know the answer is 6(x+1)^2, I'm just confused as to how to get there.

Question 443756: Would you please show me the STEPS to factor the following: 6x^2+12x+6. I know the answer is 6(x+1)^2, I'm just confused as to how to get there.
Found 3 solutions by rwm, swincher4391, josmiceli:
Answer by rwm(914)   (Show Source): You can put this solution on YOUR website!
factor out the obvious 6
6*(x^2+2x+1)
now we want factors of 1 that add up to 2
the only factors of one are 1 and 1 which add up to 2
6*(x+1)*(x+1) which is
6*(x+1)^2
Answer by swincher4391(1107)   (Show Source): You can put this solution on YOUR website!
Notice that each term has a common factor of 6.
Then you can factor it in this way
From there factor the quadratic you are presented: Since 1*1 =1 and 1+1 =2, then we can factor this into
Then the total factorization is :

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!

Divide both sides by

Use the quadratic formula

This is called a double root, since the
equation must have 2 roots, it has the same
root twice. Plug it back in for to check.
Rewrite it as:
1st factor
2nd factor
answer
Note that after you multiply it out as

Multiplying both sides by doesn't change anything

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