If sum of two polynomials is 5c² – 6c and one of the polynomials is -2c + 4c² + 1, what is the other binomial?

To find the other polynomial, we can set up the equation based on the information given:

Let the other polynomial be ( P(c) ).

We know:

[ P(c) + (-2c + 4c^2 + 1) = 5c^2 – 6c ]

We can rearrange this to find ( P(c) ):

[ P(c) = (5c^2 – 6c) – (-2c + 4c^2 + 1) ]

Simplifying further:
1. Distribute the negative:

[ P(c) = 5c^2 – 6c + 2c – 4c^2 – 1 ]
2. Combine like terms:

[ P(c) = (5c^2 – 4c^2) + (-6c + 2c) – 1 ]

[ P(c) = 1c^2 – 4c – 1 ]

So the other polynomial is:

[ c^2 – 4c – 1 ]

Therefore, the correct answer is:

c² – 4c – 1.

If you have more questions or need further clarification, feel free to ask!