I need help with this problem thanks.
Directions: Factor each plynomial. If the polynomial cannot be factrored, write prime.
m^2+8m+16
Did you not read my response to your question in
http://www.jiskha.com/display.cgi?id=1238957436 ?
To factor the polynomial m^2 + 8m + 16, we need to look for two numbers whose sum is 8 (the coefficient of the middle term, 8m) and whose product is 16 (the constant term, 16).
Let's try to find those two numbers:
1. List all the factors of 16: 1, 2, 4, 8, 16.
2. Since the sum should be positive (8), let's focus on pairs of factors that add up to 8.
- The pair of factors that add up to 8 is 4 and 4.
Now we can rewrite the middle term (8m) as the sum of two terms using the two numbers we found:
m^2 + 4m + 4m + 16
Next, we group terms to find common factors:
(m^2 + 4m) + (4m + 16)
Now, we factor out the common factors from each group:
m(m + 4) + 4(m + 4)
Notice that (m + 4) is common to both terms. We can now factor out (m + 4) from both groups:
(m + 4)(m + 4)
Simplifying, we find that the factored form of the polynomial m^2 + 8m + 16 is (m + 4)(m + 4) or simply (m + 4)^2.