n^2+8n+12
factoring
(n+ 6)(n+ 2)
To factor the expression n^2 + 8n + 12, we need to find two binomials that, when multiplied, give us the original expression.
Step 1: Look at the coefficient of n^2, which is 1.
Step 2: Find two numbers that multiply to give 1 * 12 = 12 and add up to the coefficient of n, which is 8.
The numbers that meet these conditions are 6 and 2, as 6 * 2 = 12 and 6 + 2 = 8.
Step 3: Rewrite the original expression by splitting the middle term (8n) using these two numbers:
n^2 + 6n + 2n + 12
Step 4: Factor by grouping. Group the first two terms and the last two terms together:
(n^2 + 6n) + (2n + 12)
Step 5: Factor out the greatest common factor from each group:
n(n + 6) + 2(n + 6)
Step 6: Notice that both groups have a common factor of (n + 6). Factor it out:
(n + 6)(n + 2)
So, the factored form of n^2 + 8n + 12 is (n + 6)(n + 2).