\frac{p+5+p^3\left(-p-5\right)}{-p-5}=

VJesus12 wrote:$$\frac{p+5+p^3\left(-p-5\right)}{-p-5}=$$ A. p+5+p^3
B. P^3+5
C. p^3
D. p^3-1
E. p^3-5

The OA is D.

Experts, can you help me here. I don't have it clear.

Let's just focus on the NUMERATOR for a second.
Given: p + 5 + p³(-p - 5)
Factor -1 from the first part to get: -1(-p - 5) + p³(-p - 5)
So, we now have: -1(-p - 5) + p³(-p - 5)
Combine terms to get: (-1 + p³)(-p - 5)
Rearrange terms to get: (p³ - 1)(-p - 5)

Now replace ORIGINAL numerator with (p³ -1)(-p - 5)
We get: (p³ - 1)(-p - 5)/(-p - 5)
Simplify to get: (p³ - 1)
Answer: D

Cheers,
Brent

VJesus12 wrote:$$\frac{p+5+p^3\left(-p-5\right)}{-p-5}=$$ A. p+5+p^3
B. P^3+5
C. p^3
D. p^3-1
E. p^3-5

We're looking for an expression that is equivalent to the original expression.
So if we evaluate the original expression for a particular value of p, then the equivalent expression should also yield the same value when we plug in the same value of p.
Let's test p = 1

Take: [p + 5 + p³(-p - 5)]/[-p - 5]
Replace p with 1 to get: [1 + 5 + 1³(-1 - 5)]/[-1 - 5]
Evaluate to get: 0/-6, which equals 0

So, when p = 1, the original express evaluates to be 0
Now let's plug p = 1 into the answer choices....
A. 1 + 5 + 1^3 = 7. No good, we want 0. ELIMINATE.
B. 1^3 + 5 = 6. No good, we want 0. ELIMINATE.
C. 1^3 = 1. No good, we want 0. ELIMINATE.
D. 1^3 - 1 = 0. Great - KEEP
E. 1^3 - 5 = -4. No good, we want 0. ELIMINATE.

Answer: D

Cheers,
Brent