What is the result of adding the polynomials (2x^2 + 3x - 4) and (x^2 - 5x + 6)?

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Question: What is the result of adding the polynomials (2x^2 + 3x - 4) and (x^2 - 5x + 6)?

Options:

Correct Answer: 3x^2 - 2x + 2

Solution:

When adding the polynomials, combine like terms: (2x^2 + x^2) + (3x - 5x) + (-4 + 6) = 3x^2 - 2x + 2.

What is the result of adding the polynomials (2x^2 + 3x - 4) and (x^2 - 5x + 6)?

What is the result of adding the polynomials (2x^2 + 3x - 4) and (x^2 - 5x + 6)?

Step 1: Write down the two polynomials you want to add: (2x^2 + 3x - 4) and (x^2 - 5x + 6).
Step 2: Identify the like terms in both polynomials. Like terms are terms that have the same variable raised to the same power.
Step 3: The like terms are: 2x^2 and x^2 (both are x^2 terms), 3x and -5x (both are x terms), and -4 and 6 (both are constant terms).
Step 4: Add the coefficients of the like terms together: For x^2 terms: 2 + 1 = 3, for x terms: 3 + (-5) = -2, and for constant terms: -4 + 6 = 2.
Step 5: Write the result by combining the sums of the like terms: 3x^2 - 2x + 2.
Step 6: The final result of adding the polynomials is 3x^2 - 2x + 2.

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