f(x)=x^2+7x and g(x)=x-4. FInd (f/g)(x) and (f/g)(-1)
To find (f/g)(x), we need to divide f(x) by g(x):
(f/g)(x) = f(x) / g(x)
Given that f(x) = x^2 + 7x and g(x) = x - 4, we can substitute these values into the division expression:
(f/g)(x) = (x^2 + 7x) / (x - 4)
To simplify this expression, we can perform polynomial long division or use synthetic division.
Let's perform polynomial long division:
_______________
(x - 4) | x^2 + 7x + 0
- x^2 + 4x
__________
3x + 0
- 3x + 12
______
12
The result of the polynomial long division is 3x + 12, so (f/g)(x) = 3x + 12.
To find (f/g)(-1), we substitute x = -1 into the expression (f/g)(x):
(f/g)(-1) = 3(-1) + 12
= -3 + 12
= 9
Therefore, (f/g)(-1) = 9.