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When the expression 1 - x + 2x^2 - 2 + 3x - 3x^2 + 4 - 4x + 5x^2 is written in the form ax^2 + bx + c, where a, b, and c are non-zero integers, what is the value of a + b + c?

User Bane
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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.

User Jeffresc
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