factor
1)n^2+8n+12
2)5a^2+11a+15
To after these use the FOIL method.
1. (n+2)(n+6)
You try number 2
To factor these, use the FOIL method.
Sorry typo.
To factor the given expressions:
1) To factor n^2 + 8n + 12:
First, look for two numbers whose product is equal to 12 and whose sum is equal to 8 (coefficient of n).
The factors of 12 are: 1, 2, 3, 4, 6, and 12.
Next, we need to find the pair of numbers whose sum is 8. By trial and error, we see that 2 and 6 add up to 8.
Now, rewrite the expression by splitting the middle term using these two factors:
n^2 + 2n + 6n + 12
Now, group the terms:
(n^2 + 2n) + (6n + 12)
Factor out the greatest common factors from each group:
n(n + 2) + 6(n + 2)
Notice that (n + 2) is common to both terms, so factor it out:
(n + 2)(n + 6)
Therefore, the factored form of n^2 + 8n + 12 is (n + 2)(n + 6).
2) To factor 5a^2 + 11a + 15:
Again, look for two numbers whose product is equal to 5 * 15 = 75 and whose sum is equal to 11 (coefficient of a).
The factors of 75 are: 1, 3, 5, 15, 25, and 75.
By trial and error, it may take a few attempts to find the pair of numbers whose sum is 11. In this case, the factors are 3 and 25.
Now, rewrite the expression by splitting the middle term using these two factors:
5a^2 + 3a + 8a + 15
Group the terms:
(5a^2 + 3a) + (8a + 15)
Factor out the greatest common factors from each group:
a(5a + 3) + 5(8a + 15)
Notice that (5a + 3) is common to both terms, so factor it out:
(5a + 3)(a + 5)
Therefore, the factored form of 5a^2 + 11a + 15 is (5a + 3)(a + 5).