factor the expression
x^2-7x+10 show your work
To factor the expression x^2 - 7x + 10, we want to find two terms that multiply together to give 10 and add or subtract to give -7.
The factors of 10 are 1 and 10, or -1 and -10, or 2 and 5, or -2 and -5.
We are looking for a combination that adds or subtracts to -7. The combination that works is -2 and -5, because -2 + (-5) = -7.
So, we can rewrite the expression as:
x^2 - 7x + 10 = (x - 2)(x - 5)
Thus, the expression x^2 - 7x + 10 factors to (x - 2)(x - 5).