Fully factor both of the expressions below.
a) x/2 - 17x + 72
b) 10x/2 + x - 3
a) x/2 - 17x + 72
To factor this expression, first look for common factors among the terms. There is no common factor among all the terms. However, we can factor out a common factor from the first two terms:
x/2 - 17x + 72 can be rewritten as (1/2)x - 17x + 72
The common factor between (1/2)x and -17x is x. Factoring out x, we get:
x(1/2 - 17) + 72
Simplifying further, we get:
(x/2 - 17x + 72)
Now we can factor out a common factor from the remaining terms. The common factor between (1/2) and 72 is 1/2. Factoring out 1/2, we get:
(x/2 - 17x + 72) = 1/2(x - 34)(x - 2)
Therefore, the fully factored expression is 1/2(x - 34)(x - 2).
b) 10x/2 + x - 3
First, simplify the expression:
10x/2 + x - 3 = 5x + x - 3
To factor this expression, look for common factors among the terms. There is no common factor among all the terms. However, we can factor out a common factor from the first two terms:
5x + x - 3 can be rewritten as 5x + x - 3
The common factor between 5x and x is x. Factoring out x, we get:
x(5 + 1) - 3
Simplifying further, we get:
(x + 6) - 3
Now the expression is fully factored as:
(x + 6) - 3 = x + 3
Therefore, the fully factored expression is x + 3.