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

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

Options:

Correct Answer: 7x^2 - x + 4

Solution:

Adding the two polynomials gives (3x^2 + 4x^2) + (2x - 3x) + (-1 + 5) = 7x^2 - x + 4.

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

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

Step 1: Write down the two polynomials you want to add: (3x^2 + 2x - 1) and (4x^2 - 3x + 5).
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: Group the like terms together: (3x^2 + 4x^2), (2x - 3x), and (-1 + 5).
Step 4: Add the coefficients of the like terms: For x^2 terms: 3 + 4 = 7, for x terms: 2 - 3 = -1, and for constant terms: -1 + 5 = 4.
Step 5: Write the result by combining the sums of the like terms: 7x^2 - x + 4.

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