Find the sum of 3x^2 - x + 8 and 5x - 1.
Understand the Problem
The question is asking for the sum of two polynomials: (3x^2 - x + 8) and (5x - 1). We will combine like terms to find the final result.
Answer
The sum is \(3x^2 + 4x + 7\).
Answer for screen readers
The sum of the two polynomials is (3x^2 + 4x + 7).
Steps to Solve
- Identify the polynomials to be summed
The problem provides us with the two polynomials: [ 3x^2 - x + 8 \quad \text{and} \quad 5x - 1 ]
- Align the like terms
Next, we need to line up the like terms in both polynomials:
- Quadratic term: (3x^2)
- Linear terms: (-x + 5x)
- Constant terms: (8 - 1)
- Combine the like terms
Now we can combine the like terms:
- Quadratic term: (3x^2)
- Linear terms: (-x + 5x = 4x)
- Constant terms: (8 - 1 = 7)
So, the combined expression becomes: [ 3x^2 + 4x + 7 ]
The sum of the two polynomials is (3x^2 + 4x + 7).
More Information
Combining polynomials involves adding their like terms (terms with the same degree). This operation is fundamental in algebra and is key to simplifying expressions.
Tips
- Forgetting to combine all like terms: Ensure you group together all similar terms.
- Incorrect signs: Double-check that the signs of each term are correct while adding or subtracting.
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