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What is the result of adding the polynomials 3x^2 + 2x - 1 and 2x^2 - 5x + 4?

a. 5x^2 - 3x + 5
b. 5x^2 - 7x + 3
c. 6x^ - 3x + 3
d. 5x^2 - 3x + 3

1 answer

To add the polynomials \(3x^2 + 2x - 1\) and \(2x^2 - 5x + 4\), we combine like terms.

  1. Combine the \(x^2\) terms: \[ 3x^2 + 2x^2 = 5x^2 \]

  2. Combine the \(x\) terms: \[ 2x - 5x = -3x \]

  3. Combine the constant terms: \[ -1 + 4 = 3 \]

Putting it all together, we get: \[ 5x^2 - 3x + 3 \]

The correct answer is: d. \(5x^2 - 3x + 3\)