Final answer:
The correct difference of the given algebraic expressions is found by combining like terms and simplifying over the common denominator, resulting in the answer 11p^2 + 6p + 2 over 4p^2.
Option c.
Step-by-step explanation:
The problem given is a simplification of algebraic expressions, which can be solved by combining like terms and simplifying.
We're asked to find the difference of p^2 + 6p + 2 and -10p^2, both over a denominator of 4p^2. To find this difference, you subtract the numerators while keeping the common denominator:
First, combine like terms in the numerator: (p^2 + 6p + 2) - (-10p^2) becomes p^2 + 10p^2 + 6p + 2, as subtracting a negative is the same as adding.
Then, simplify the combined terms: p^2 + 10p^2 is 11p^2, so the numerator is now 11p^2 + 6p + 2.
Finally, write the simplified expression over the original denominator: 11p^2 + 6p + 2 over 4p^2.
The correct answer is therefore option (c) 11p^2 + 6p + 2 / 4p^2.