Option C: 
is the product of the rational expression.
Explanation:
The given rational expression is 
We need to determine the product of the rational expression.
<u>Product of the rational expression:</u>
Let us multiply the rational expression to determine the product of the rational expression.
Thus, we have;
Let us use the identity 
in the above expression.
Thus, we get;
Simplifying the terms, we get;
Thus, the product of the rational expression is
Hence, Option C is the correct answer.
First, let's factor the equation to make it easier to solve for the intercepts:
f(x) = x² + 12x + 32
f(x) = (x + 8)(x + 4)
To find the x-intercepts of a function, set the y value (f(x)) to 0:
0 = (x + 8)(x + 4)
x = -8, -4
Similarly, to find the y-intercept, set the x values to 0:
f(x) = (0 + 8)(0 + 4)
f(x) = (8)(4)
f(x) = 32
*Note that you can see 32 as the y-intercept in the parabola's original equation
1.) expand
3x - 15 - 5x = 25 + 6x
2.) simplify
-2x - 15 = 25 + 6x
3.) add 2x to both sides
-15 = 25 + 6x + 2x
4.) simplify
-15 = 25 + 8x
5.) subtract 25 from both sides
-15 - 25 = 8x
6.) simplify -15 - 25 to -40
-40 = 8x
7.) divide both sides by 8
-40/8 = x
8.) x = -5
The ball will hit the ground when h(t)=0 so:
16t^2-96t=0
16t(t-6)=0, since t>0
t=6
So the ball with hit the ground after 6 seconds.
