factor the expression x^2-7x+10
show work step by step
To factor the expression x^2 - 7x + 10, we need to find two numbers whose sum is -7 and whose product is 10. We can do this by factoring the trinomial.
First, we look at the coefficient of the x^2 term, which is 1. Since it is positive, we know that both factors must have the same sign.
Next, we look at the constant term, which is 10. We need to find two numbers whose product is 10 and whose sum is -7.
The two numbers that meet these conditions are -2 and -5. -2 multiplied by -5 is 10, and -2 plus -5 is -7.
So, we can rewrite the trinomial as:
x^2 - 7x + 10 = (x - 2)(x - 5)
Thus, the expression x^2 - 7x + 10 is factored as (x - 2)(x - 5).