write the expression in lowest terms:
y^2+2y-8/y^2+5y-14
How do u do this problem?
Glad to see you know calculus.
Factor the numerator, and denominator. There probably will be a common factor that will divide out.
I asked the question and when i hit submit it hit me, it was a very easy problem!!
To simplify the given expression in lowest terms, you need to factor both the numerator and the denominator and then cancel out any common factors.
1. Factor the numerator:
The numerator is the quadratic trinomial y^2 + 2y - 8. To factor this, we need to find two numbers whose product is equal to the product of the coefficient of y^2 (1) and the constant term (-8), and whose sum is equal to the coefficient of y (2).
The factors of -8 that meet this criteria are -4 and +2.
Therefore, we can rewrite the numerator as (y - 2)(y + 4).
2. Factor the denominator:
The denominator is another quadratic trinomial, y^2 + 5y - 14. Again, we need to find two numbers whose product is equal to the product of the coefficient of y^2 (1) and the constant term (-14), and whose sum is equal to the coefficient of y (5).
The factors of -14 that meet this criteria are -7 and +2.
Therefore, we can rewrite the denominator as (y - 2)(y + 7).
3. Cancel out the common factors:
Now that we have factored both the numerator and denominator, we can cancel out any common factors between them.
In this case, we have (y - 2) as a common factor in both the numerator and denominator.
By canceling it out, we get the simplified expression: (y + 4) / (y + 7).
So, the given expression, (y^2 + 2y - 8) / (y^2 + 5y - 14), in lowest terms is (y + 4) / (y + 7).