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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)?
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Q1
What is the result of adding the polynomials (3x^2 + 2x - 1) and (4x^2 - 3x + 5)?
7x^2 - x + 4
7x^2 - x - 6
x^2 - x + 4
x^2 + 5
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Adding the two polynomials gives (3x^2 + 4x^2) + (2x - 3x) + (-1 + 5) = 7x^2 - x + 4.
Questions & Step-by-step Solutions
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Q
Q: What is the result of adding the polynomials (3x^2 + 2x - 1) and (4x^2 - 3x + 5)?
Solution:
Adding the two polynomials gives (3x^2 + 4x^2) + (2x - 3x) + (-1 + 5) = 7x^2 - x + 4.
Steps: 5
Show Steps
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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