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

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

Options:

Correct Answer: 7x^2 + 4x + 6

Solution:

Adding the two polynomials gives (2x^2 + 5x^2) + (3x - x) + (4 + 2) = 7x^2 + 2x + 6.

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

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

Step 1: Write down the two polynomials you want to add: 2x^2 + 3x + 4 and 5x^2 - x + 2.
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. The like terms are: 2x^2 and 5x^2, 3x and -x, and 4 and 2.
Step 4: Add the coefficients of the like terms. For 2x^2 and 5x^2, add 2 + 5 to get 7, so you have 7x^2.
Step 5: For the x terms, add 3 and -1 (since -x is the same as -1x) to get 3 - 1 = 2, so you have 2x.
Step 6: For the constant terms, add 4 and 2 to get 4 + 2 = 6.
Step 7: Combine all the results from the previous steps to write the final polynomial: 7x^2 + 2x + 6.

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