if possibly completely factor the factor the expression(if the polynomial is not factorable using integers enter prime)
x^2+10x+16
(x+8)(x+2)
To completely factor the expression x^2 + 10x + 16, we need to find two binomials whose product equals the given expression.
First, we look for two numbers whose sum is 10 and whose product is 16. Let's call these numbers a and b. The binomials can then be written as (x + a)(x + b).
We have a few options for a and b that sum to 10 and multiply to 16: (1, 16), (2, 8), and (4, 4).
Now, we check if any of these options can be factored using integers.
For (1, 16):
(x + 1)(x + 16) - This expression cannot be factored any further using integers.
For (2, 8):
(x + 2)(x + 8) - This expression cannot be factored any further using integers.
For (4, 4):
(x + 4)(x + 4) - This expression can be factored further using integers.
Therefore, the completely factored form of the expression x^2 + 10x + 16 is (x + 4)(x + 4).