Final answer:
The given expression simplifies to 4x^2 - 2x + 3. When written as ax^2 + bx + c, we find that a = 4, b = -2, and c = 3. Therefore, the sum a + b + c is 5.
Step-by-step explanation:
To simplify the expression 1 - x + 2x^2 - 2 + 3x - 3x^2 + 4 - 4x + 5x^2 into the form ax^2 + bx + c, we need to combine like terms. This involves adding/subtracting the coefficients of the terms with the same power of x.
First, we combine the x^2 terms: (2x^2 - 3x^2 + 5x^2) which equals 4x^2.
Next, we combine the x terms: (-x + 3x - 4x) which equals -2x.
Finally, we add the constant terms: (1 - 2 + 4) which equals 3.
The expression in the form ax^2 + bx + c is 4x^2 - 2x + 3. Now, we find the value of a + b + c, which is 4 - 2 + 3 equals 5.