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

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

Options:

Correct Answer: 6x^2 + 4x + 5

Solution:

Adding the coefficients of like terms gives 6x^2 + 2x + 5.

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

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

Step 1: Identify the two polynomials you want to add: 2x^2 + 3x + 4 and 4x^2 - x + 1.
Step 2: Write down the like terms from 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 4x^2 (for x^2 terms), 3x and -x (for x terms), and 4 and 1 (for constant terms).
Step 4: Add the coefficients of the like terms together: 2 + 4 = 6 for x^2 terms, 3 + (-1) = 2 for x terms, and 4 + 1 = 5 for constant terms.
Step 5: Write the result as a new polynomial by combining the sums of the like terms: 6x^2 + 2x + 5.

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