"If possible, completely factor the expression. (If the expression is not factorable, enter NF.) x2 − 6x − 7"
the factors of -7 are
-1 and 7
1 and -7
can you pick them so they add up to -6?
(x+1)(x-7)
(If the expression is nonfactorable over the integers, enter NONFACTORABLE.)
y2 − 5y + 25
To completely factor the expression x^2 - 6x - 7, we need to find two binomials that multiply together to give us the original expression.
First, we look for two numbers whose product is -7 and whose sum is -6 (the coefficient of x). The numbers that satisfy these conditions are -7 and 1. Therefore, we can rewrite the expression as:
x^2 − 7x + x − 7
Now, we group the terms and factor out the greatest common factor from each pair:
x(x - 7) + 1(x - 7)
Notice that we now have a common binomial (x - 7). Therefore, we can factor it out:
(x + 1)(x - 7)
So the completely factored form of the expression x^2 - 6x - 7 is (x + 1)(x - 7).