X2-7x-12/x-2
do you mean (x^2-7x-12)/(x-2)?
break it down:
(x^2-7x)/(x-2)
let's try x in order to eliminate the x^2
(x^2-7x)-(x^2-2x)=-5x
carry down the -12, so you'll have:
(-5x-12)/(x-2)
how would I eliminate -5x? what should I multiply (x-2) to by in order to eliminate -5x? (hint: x times what equals -5x?)
not much can be done with it, if you wanted it simplified
(x^2 - 7x - 12)/(x-2)
= (x-3)(x-4)/(x-2) , noting cancels here.
or
you can do either a long divsison or synthetic division to get
(x^2 - 7x - 12)/(x-2)
= (x-5) - 2/(x-2)
To simplify the expression (x^2 - 7x - 12) / (x - 2), we can factor the numerator and simplify further.
Step 1: Factor the numerator (x^2 - 7x - 12):
We want to find two binomials that multiply to give us the numerator x^2 - 7x - 12. We can use the factoring method or the quadratic formula to find the factors.
The factors of -12 are:
1 and -12
-1 and 12
2 and -6
-2 and 6
3 and -4
-3 and 4
Among these factors, we need to find the pair that sums up to -7 (the coefficient of the x term). The pair of factors that satisfy this is -3 and 4.
Thus, we can rewrite the numerator as (x - 3)(x + 4).
Step 2: Simplify the expression:
Now that we have factored the numerator, we can rewrite the expression as:
(x^2 - 7x - 12) / (x - 2) = ((x - 3)(x + 4)) / (x - 2)
The expression is now simplified and cannot be further reduced.